The system you want exists, just not in pen and paper:
http://www.ckiiwiki.com/Opinion

Crusader Kings 2 has a relatively sophisticated system of modifiers that determines another character's opinion of the player character, based on many different factors. These are usually divided into group modifiers (things about your character that will affect many other characters), and individual modifiers (usually actions that your character has taken to aid/hurt an NPC).
Group Modifiers
Can be positive or negative, and may affect certain groups of NPCs differently.
Examples:
- Personal diplomacy (+ or - depending on player's attributes). Affects all NPCs.
- Short reign (-). Affects every NPC's opinion of that character.
- Foreigner (-). Affects only NPCs in a different cultural group to the PC.
- Kinslayer (-). Affects only members of the PC's family.
- Religious differences (-). Affects only NPCs of a different religion. Sharing a religion with an NPC has a corresponding positive modifier.
- Shared/different trait (- or +). If the PC and an NPC are both charitable, the NPC will like the player more. If they have opposite traits, however (charitable vs greedy), the modifier is negative.
And so on and so forth. This is where you would have to decide how complex you needed your opinion system to be. What kind of things exist in your game that are a big deal to the NPCs? Is there a bias against magic users? Give NPCs a negative modifier towards the party if they have a wizard.
Individual Modifiers
These are bonuses or penalties applied to the character's relationship with a specific NPC. They may have a time limit associated with them (3 months before the favor is forgotten, for example).
Examples:
- Pressed my claim (+80)
- Imprisoned the NPC (-30)
- Murdered my child (-100)
- Gave me a gift (+10)
There are also passive bonuses or negatives for the type of relationship the PC shares with an NPC:
- Same dynasty (+50)
- Half-brother (-40). The NPC might only have this applied if he's also a contender for the throne. In the party's case, this would be a political or social rival.
In the case of individual modifiers, it's probably not possible to have pre-defined ones for every situation that the party can get into. Rather, you would keep track of who the party is cheating or aiding, and apply appropriate modifiers after the fact. Possibly assign them a time limit (either # of sessions, or in-game time) before that bonus expires.
Keeping Track of It All
I could see creating a spreadsheet of NPCs to keep track of these various modifiers, possibly summing each column at the bottom for easy reference. The benefit of this approach would be having only one document to maintain.
Another alternative would be loading up a program like One Note or Evernote, and creating a note for each NPC you want to keep track of. Put their current modifiers at the bottom of the page (I believe both programs have a table that can do automatic sums), and update your NPCs at the end of each session. This would probably be my approach, since I would tend to lose track of individual NPCs if I kept them in the same sheet together.
Alternatives?
It's important to remember that Crusader Kings 2 can get away with this kind of thing because it is a video game -- this sort of detailed opinion system might be a little much to keep track of by hand. For a tabletop game, perhaps it could be streamlined a bit:
- Grab an index card for each NPC you want to keep track of.
- Add + or - to the card, based on events/traits/whatever you want. Assign more ++ or --- to specific things.
- Count the + and - modifiers at the end and decide an overall score.
- Cross out modifiers that no longer apply.
Example:
Jace Windu (Alien bounty-hunter)
- Party is all humans (-)
- Party cheated him (---) 6 sessions |||
- Party works for the same crime organization (+)
- Party has a fearsome street rep (+)
Total: --
For the second modifier, you can see that I am keeping track of the number of sessions that have passed (3) with tick marks. In 3 more sessions, Jace will lose the cheated modifier on his own. Alternatively, the party could try to mend fences with him and remove that modifier earlier. OR they could cheat him again, leading to the removal of the old modifier and the addition of a permanent Grudge modifier (-----) that will probably motivate Jace to seek revenge at some point.