Ok, so you have a general with 7 loyalty who is a Man of Principle (+50% to bribe cost). He's commanding an army of UM and Archers?
What is the size and make up of the army he's commanding? What is his Command stat (I think this affects bribe cost of the general's unit)? Finally - are all of the units in the province in one single stack? Putting them all in one stack makes it more expensive for the enemy to bribe the stack as they have to "buy" all the units in the stack.
If you can't stop the enemy bribing his stack because the AI has money coming out his ears, split the stack up into individual units so only one can be bribed at a time per diplomat and MOVE ALL UNITS OUT OF YOUR GARRISON.
If the garrison unit gets bribed, you'll lose the province, so the easiest way to avoid this is to have no units in the castle.
Let me know how this works for you. Unless he brings in an army of diplomats so he can bribe multiple untis a turn, you should be able to keep the province safe from being bought off you.
Side issue: If money is tight, don't bother with any more archers, they are expensive to build and upkeep. Focus on more UM. These are cheap and nasty with 2 AP attack and 4 Charge so can pack a bit of offensive punch.
If the AI is styupid enough to try and bribe your units 1 at a time, your other forces will slaughter the turn coat easily.
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