ACKs tends to minimise the need for ability score bonuses compared to other systems, as such I have been considering rules without them.
Not much really needs to be changed and I have a few possible ideas. These generally revolve around that in many cases characters overall end up with about a +2 bonus across the board on average (this presumes the 5 character start up). This gives some modifications but not really a huge number.
This essentially works on the basis that a character is better than average in what the character does. Essentially characters get an equivlent of +2 across their prime requsites to determine the alterations of that ability score to other values. Thus a fighter would gain +2 to melee hit and damage, +8 to open doors and +2 stone to overloaded (all the things strength tends to add). A mage gains +2 general proficiencies, +2 languages and +2 repertoire spells per level (ie. bonuses +2 intelligence would give). While a Spellsword would gain +1 to melee hit and damage, +4 to open doors, +1 stone to overloaded, +1 general proficieny +1 language and +1 repertoire spell per level (all the things +1 strength and +1 intelligence would modify).
The downside to this however is that classes become rather homoginised in their core aspects where ability scores are concerned and still have some minor link to ability scores.
Similar to Prime Factors, this works on the basis that characters get the alterations to other stats that an ability score bonus would otherwise give. However a character rolls a d6 twice, and gains the equivlent of +1 to that ability score for the derived values. 1. Strength, 2. Intelligence, 3. Wisdom, 4. Dexterity, 5. Constitution and 6. Charisma.
Thus if a character rolled a 2 and a 6, they would get +1 general proficency, + 1 language, (+1 repotiore per level), +1 to reaction rolls and 1 additional henchman they can employ.
The downside to this is it has some link still to ability scores.
My preferred method however is traits. This gives a small package of bonuses to the various alternate stats often modified by ability scores. A character rolls for these twice and the trait bonuses can stack (or not if that is desired).
As part of this though arcane casters miss a little in their repertoire (often having an intelligence bonus), thus Mages (and other pure arcane casters) gain 2 additional repertoire spells per level, while hybrids (like the spellsword and nightblade) gain 1 additional repertoire spells per level.
Traits: (roll a d12)
1. Alert: +1 to avoid surprise and +2 to Hear Noise or other awareness throws
2. Deft: +1 to Armour Class and +1 to initiative
3. Hardy: +1 to hit point per level and +2 bonus to poison and death savings throws
4. Intuitive: +1 to avoid surprise and +2 bonus to savings throws vs spells or magic items
5. Nimble: +1 to Armour Class and +2 bonus to breath and blast savings throws
6. Perceptive: +1 to hit for missile attacks and +2 when searching (eg, traps, secret doors, tracking and so forth)
7. Prowess: +1 to hit for melee and missile attacks
8. Resilient: +1 bonus to all savings throws and +2 to Mortal Wound rolls
9. Savvy: +1 general proficiency, +1 language and +2 to any lore or knowledge throws
10. Strong: +1 to melee damage, +4 to open doors and +1 overloaded encumbrance
11. Suave: +1 to reaction rolls and +2 to maximum Henchman
12. Willful: +2 bonus to savings throws vs charm, fear, illusions and resisting intimidation or any other composure throws
Adept: +2 Cleaves and +1 level for spell casting effects
Bulwark: +1 Armour Class and +1 hit point per level
Heirloom: You start with a magic or special item of considerable value (discuss with GM as to specifics)
Linguist: +1 to reaction rolls when you speak, +4 languages
Lucky: Twice per day you can re-roll any failed Throw, but must take the result of the second roll.
Talented: +1 Proficiency from any list