If you're just trying to avoid issues with the Amarr Navy, you can train up Diplomacy. (Raises your effective negative standings)
That will only help so much, though. At some point, you'll either have to start declining those particular missions, or just take the hits. If you plan on being able to fly through all Empire space, at no risk, that is.
I dont like turning down missions because I like making money.
Spoken like a true... Caldari?
You can decline one mission every four hours (without taking a standings hit, for declining).
If you get a mission that you don't like, decline it. Wait at least a minute before asking for another. (That might just be mystic voodoo, but I've found that if I re-ask too soon... I get the same mission offered again).
If you're set on using Matari agents (for the LP Store), you may even want to consider which division you are running missions for. Not all are kill-missions.