Hi veritas, I had the same problem until someone kindly pointed out that there is a little button (showing a gift-wrapped present) just to the left of the larger "Make Offer" button. This is what you use to make a gift.

The distinction is quite a good one - if you offer to hand over a certain amount of cash or a province as a gift, the AI will gratefully accept; if you offer the same but don't make it a gift, the AI will assume you expect something in return - and will be rightfully suspicious.

You should find diplomacy working much better for you in the future!