Various ideas about how to rework the existing stones.

[The Warrior]
Last Seed
The Warrior is the first Guardian Constellation and he protects his charges during their Seasons. The Warrior's own season is Last Seed when his Strength is needed for the harvest. His Charges are the Lady, the Steed, and the Lord. Those born under the sign of the Warrior are skilled with weapons of all kinds, but prone to short tempers.

[Vanilla]
Learn combat skills 20% faster

[Modded] 
Mod Power Attack Damage: power attacks do 20% more damage
Mod Power Attack Stamina: power attacks cost 20% less stamina
Mod Spell Cost: spells cost 20% more magicka
Mod Spell Magnitude: 20% reduced spell magnitude
Mod Percent Blocked: parry 20% more damage
Mod Armor Weight: equipped armor weight 20% less
Mod Detection Movement: 50% easier to be spotted when moving (since the reduced armor weight is a sneak bonus, this malus should be bigger)

[Brainstorming]
Fortify combat skills +25 (it is a skill bonus, not an xp bonus) but -10 to stealth and -20 to magic skills.

better in combat skills, worse in stealth/magic

[The Lady]
Heartfire
The Lady is one of the Warrior's Charges and her Season is Heartfire. Those born under the sign of the Lady are kind and tolerant.

[Vanilla]
Regenerate Stamina 25% faster, Regenerate Health 25% faster

[Modded]
Regenerate 1 point of health per second for each missing 20% health but lose 1 point of stamina per second (min 0, max 4).
Regenerate 1 point of stamina per second for each missing 20% stamina but lose one point of magicka per second (min 0, max 4).

[Brainstorming]
Gives the benefits of Bribery, Persuasion and Intimidation perks.
Earlier access to high level Speech perks (you don't get the real perks but similar effects)

[The Steed]
Mid Year
The Steed is one of the Warrior's Charges, and her Season is Mid Year. Those born under the sign of the Steed are impatient and always hurrying from one place to another.

[Vanilla]
Wearing armor does not affect speed, Carry Weight +100, Equipped armor is weightless

[Modded]
Decrease armor weight, increase maximum carry weight, sprint don't cost stamina. The bonus are active only during sprinting, and only at health>=80%.

[Brainstorming]
Regenerate stamina while sprinting (7/s)
Regenerate stamina while sprinting, making normal sprinting virtually infinite. Useful for -no-fast-travel- plays
remove max and equipped weight bonus

[The Lord]
First Seed
The Lord's Season is First Seed and he oversees all of Tamriel during the planting. Those born under the sign of the Lord are stronger and healthier than those born under other signs.

[Vanilla]
Armor Rating +50pts, Resist Magic 25%

[Modded]
Gain 40 points of Armor and 5% magic resistance for each missing 20% health (min 0/0%, max 160/20%)

[Brainstorming]
Cloak effect, followers gain 40 points of Armor and 5% magic resistance for each missing 20% health (min 0/0%, max 160/20%).
Increase max followers by 1, and another +1 for each completed quest line.
Increase the efficiency of allies, can have more followers.

[The Mage]
Rain’s Hand
The Mage is a Guardian Constellation whose Season is Rain's Hand when magicka was first used by men. His Charges are the Apprentice, the Golem, and the Ritual. Those born under the Mage have more magicka and talent for all kinds of spellcasting, but are often arrogant and absent-minded.
As the Dwemer didn't believe in magic, they knew this constellation as "The Mechanist" . This constellation contains the Planet Julianos, which is also called the Eye of the Sage.

[Vanilla]
Learn magic skills 20% faster

[Modded]
Increase spell cost, duration, range and magnitude by 20%.

[Brainstorming]
Increase spell cost, duration, range and magnitude by 20%.
Power attacks cost 20% more stamina and do 20% less damage.
20% less damage blocked.
20% easier to detect.
enhance spell based on equipped spell or known perks, recharge charged items and enable special crafting recipes
The Mechanist - Item recharging: gives a concentration power that sucks magicka and restore charges, or a passive/constant/toggleable with the same effect.

[The Apprentice]
Sun’s Heigh
The Apprentice's Season is Sun's Height. Those born under the sign of the apprentice have a special affinity for magick of all kinds, but are more vulnerable to magick as well.

[Vanilla]
Regenerate Magicka +100%, Weakness to Magic +100%

[Modded]
+100% magicka regeneration and -20% magic resist every missing 20% magicka
Min: +100% magicka regeneration, -20% magic resist at magicka 100%
Max: +500% magicka regeneration, -100% magic resist at magicka <=20%

[Brainstorming]
+30% magicka rate and -30% magic resist. Always active
If magicka <=60% +30% magicka rate and -30% magic resist
If magicka <=30% +40% magicka rate and -40% magic resist
each tier stack
magickarate multiply fortify magicka regeneration effects (usually it is used only by the ring of erudites); it scale with equipment and perks

[The Atronach]
Sun’s Dusk
The Atronach (often called the Golem) is one of the Mage's Charges. Its season is Sun's Dusk. Those born under this sign are natural sorcerers with deep reserves of magicka, but they cannot generate magicka of their own.

[Vanilla]
Magicka +50pts, Spell Absorption 50%, Regenerate Magicka 50% slower

[Modded]
+50 magicka, -50% magicka regeneration, 10% spell Absorption; magicka degeneration and absorption grow with missing magicka
Min: +50 magicka, -50% magicka regeneration, 10% spell Absorption at magicka 100%
Max: +50 magicka, -250% magicka regeneration, 50% spell Absorption at magicka >=20%

[Brainstorming]
+50 magicka, -50 health, -50% magicka regeneration, 10% spell Absorption; magicka degeneration and absorption grow with missing magicka
Min: +50 magicka, -50% magicka regeneration, 10% spell Absorption at magicka 100%
Max: +50 magicka, -250% magicka regeneration, 50% spell Absorption at magicka<=20%
maybe I can debuff the magickarate instead of the magickaratemult

[The Ritual]
Morning Star
The Ritual is one of the Mage's Charges and its Season is Morning Star. Those born under this sign have a variety of abilities depending on the aspects of the moons and the Divines.

[Vanilla]
Raise all dead to fight for you once a day for 200 seconds

[Modded]
You can summon one more creature, but the health of the caster is constantly drained by 50.

[Brainstorming]
constant soul trap cloak
permanent life drain
permanent magicka absorb

[The Thief]
Evening Star
The Thief is the last Guardian Constellation, and her Season is the darkest month of Evening Star. Her Charges are the Lover, the Shadow, and the Tower. Those born under the sign of the Thief are not typically thieves, though they take risks more often and only rarely come to harm. They will run out of luck eventually, however, and rarely live as long as those born under other signs.

[Vanilla]
Learn stealth skills 20% faster

[Modded]
Increase the gold and items found in chests (like the Golden Touch and Treasure Hunter perks)

[Brainstorming]
Random damage dealt and received (between 50% and 200%)
You find +/- 100% gold and +/- 100% items.
Random values have higher max but lower min.

[The Lover]
Sun’s Dawn
The Lover is one of the Thief's Charges and her season is Sun's Dawn. Those born under the sign of the Lover are graceful and passionate.

[Vanilla]
Learn all skills 15% faster

[Modded]
The usual +15% xp bonus but you cannot gain other xp bonus (rested, well rested, etc...).
If you have the blessing of Dibella (amulet, blessing or quest reward) you get another 15% bonus.
If you have the blessing of Mara (amulet, blessing or quest reward) you get another 15% bonus.
Spells and weapons do 35% less damage.

[Brainstorming]
Usual 15% bonus to all skills but cannot gain the lover, rested and well rested bonus.
Gain another 15% bonus if you have a follower and another 15% if you are married.
Learn all skills 15% faster; another 15% if the character is married, another 15% if he has a follower.
More quest/blessing related bonus.

[The Shadow]
Second Seed
The Shadow's Season is Second Seed. The Shadow grants those born under her sign the ability to hide in shadows.

[Vanilla]
Become invisible for 60 seconds once a day

[Modded]
Gain a sneak power mod based on current sneak, but decrease carry weight for the same amount.
Start at +10/-10 and max at +100/-100 at sneaking 90.

[Brainstorming]
Your worn armor weight nothing, but maximum carry weight is reduced.
(CW penalty of 25 every 50 max carry weight)
Lesser power, fortify Sneak skill based on sneak Skill but not true invisibility.
Can be used only in interior, during night, or from a shadow spot.
Light has a lesser impact on sneaking, based on Sneaking skill.

[The Tower]
Frost Fall
The Tower is one of the Thief's Charges and its Season is Frostfall. Those born under the sign of the Tower have a knack for finding gold and can open locks of all kinds.

[Vanilla]
Unlock any Expert or lower level lock instead of picking it once a day

[Modded]
Lockpicks never break.

[Brainstorming]
Various bonus in lockpicking based on the skill.

[The Serpent]
no season
The Serpent wanders about in the sky and has no Season, though its motions are predictable to a degree. No characteristics are common to all who are born under the sign of the Serpent. Those born under this sign are the most blessed and the most cursed.

[Vanilla]
Paralyze target for 5s and Damage Health of target 25pts

[Modded]
Lesser power (at will, a few seconds cooldown). Paralyze for 5 seconds, but deal no damage. Can be used only on targets out of combat.

[Brainstorming]
Lesser power, at will. Only paralyze, no damage. Works only out of combat. Cost magicka a/o stamina.
power at will, but also damage the caster
Shouts: activation power, immediately reset the shout meter but deal health/stamina/magicka damage for each second remaining; can kill the PC if used lightly, but you can shout every second if you have the attributes to do so; I fear I cannot do that without scripts