I'm not sure how it works with the AI but rejecting a demand for providing gifts usually has dire consequences. Perhaps the AI is more receptive to following demands if the player requesting has a larger army than the other side?

I wanted to use this as a way of goading AI players to unaffiliate with me so I could attack them. Or in the very least, antagonize them when they're being beaten into the ground. Better than them offering a trade agreement with me when it's down to the last planet at any rate.

There's reasearch items for this (demanding resources) for at least the Advent, but when you "Request mission" of another faction there is no option for demainding resources from them: just attacking a planet.