Do you actually say, "I want you to be my vassal", or do you just demand gold and resources? And do you do this when they only have 1 city left?
Also, it doesn't surprise me that you get backstabbed. I bet as soon as you make somebody a vassal, they immediately start talking to other powerful civs and get friendly with them. It's just like the real world, if America makes a country its vassal, chances are that country will get very friendly with Russia and China.
Maybe a good vassal strategy would be to occasionally gift a unit, that way they get a "benefit" from being a vassal. People are much less likely to bite the hand that feeds them.