OK, here are some ideas regarding perks for FO3 companions. I wrote down two ideas per companion, just in case that some ideas are bad :) I usually went for stat boosts, since I don´t know what is exactly possible to create in the GECK.
Here is my list:
Star Paladin Cross (Human)(good):
Sister of steel: Star Paladin Cross can be "disabled" by EMP effects. If hit by an EMP effect she becomes unconscious for the remainder of combat.
Survivor instinct: Having survived against all odds and protected the Lone wanderers life as a child she raises DT by 10 while she accompanies the player.
Fawkes (Super Mutant)(good):
Mutant Castaway: When fighting against other super mutants Fawkes´ damage is increased by 10%
Explosives "Guy": When Fawkes health drops bellow 50%, his explosives Skill is increased to 100.
Butch DeLoria (Human)(neutral):
Entomophobia: When fighting against mutated insects (Rad Roaches, Giant Ants, Rad Scorpions) Butch will flee until the combat is over.
Figaro: While using sharp meele weapons Butch´s crit chance is increased by 25%
Clover (Human)(evil):
Pain in the neck: While wearing her slave collar, Clover´s damage is increased by 5%.
Beast unleashed: While not wearing her slave collar, Clover sometimes get´s a psychotic episode, when her health is lower than 50% (this could work like lily´s episodes)
Jericho (Human)(evil):
Smoking gun: After giving Jericho a pack of cigarettes his gun damage is increased by 5% for 5 realtime minutes.
Knowing their lifestyle: While Jericho accompanies the player, any damage done against raiders is increased by 5%
Charon (Ghoul)(any):
Contract Killer: While Charon accompanies the player, any damage done against humans & ghouls is increased by 5%.
Bodyguard: If the players HP drop below 25% Charon tries to shield the player, raising the players DT by 5. (could work similar like the "nerd rage!" perk)
Seargeant RL-3 (Robot)(Neutral):
Death to the communists! While fighting chinese remnants Seargent RL-3 becomes frenzied (25% crit?).
Engineer! I´m rusting!: When Seargent RL-3s Hitpoints drop below 25% his DT is raised by 5 for the remainder of the fight.
Dogmeat (Animal)(Any):
Protective instinct: When the player is hurt while wearing the tunnel snake outfit, leather armor or roving trader outfit Dogmeat becomes frenzied (+25% crit?).
Sniffin´ it out: While Dogmeat accompanies the player there is a small chance to find more caps and ammunition in containers (10% Chance for double caps or double ammo, should work in a similar way like the perks "fortune finder" and "scrounger")