Came across this more by luck than anything. Was looking around for guides on improving reputation without having to mess with game files, then read one that claimed that offering to attack rebels and then doing so improves reputation.
Started up a game, made a few allies, then started bartering to attack the rebel faction. Only gets me a few hundred gold for the work, but then again it’s not like I wouldn’t have to take care of the issue anyways.
Where things get strange is that things actually worked the opposite way around. Bit by bit I notice my allies’ reputations steadily improving with each completed “deal” of attacking some rebels.
Start up another game, cheat in some money (because naturally the AI offers hundreds yet demands thousands), start sending out diplomats everywhere, and go around paying the various AI to go rebel-hunting.
Lo and behold, with enough of these weird little deals (Somewhere in the 8-10 range) my reputation is almost perfect by turn 10 (On Normal difficulty, for reference). Also improved diplomatic relations in the process, although that may be more to letting the AI decide the payment without trying to haggle.
Pay the AI to attack rebels for easy (albeit a little pricey) reputation boost.