Well an alliance is like friendship, but its voluntary and each state retains total rights to itself. While a vassalage could involve getting some benefits from your host state and sending taxes back to your host state. It could be an even closer version of an alliance if people willingly partake. (But unlike an alliance can be forced on a player). I think that a vassalage mechanic could allow some degree of control over your vassal. For instance, you can outlaw a certain religion within your vassal states and you can adjust the taxes from near nothing to downright tyrannical. I think you should also be able to take peoples luxury and strategic resources from them too (If you choose). This way you could make actual colonies out of players. Perhaps you can have builders make things on their territory as well.
So here are two example situations:
1. You have a friend who is severely behind you in just about everything. So you decide to adopt them as your vassal and you immediately go in and start building improvements for them with some of your builders. You tax them a meager 1 gold per turn and leave them total freedom of religion and resources. Perhaps by being the vassal of a bigger country they will research things faster as well.
2. You want to put a colony on America, but the indigenous backwards Americans (Teddy) have already taken up all of the continent. You are far more powerful but don't want to conquer them downright, so you destroy a few of their coastal cities then force them to become a vassal. As a vassal you force them to pay 20 gold per turn and to give all of their tobacco and cotton resources. You also outlaw their backwater religions (Which just lowers the pressure from it) and keep troops across their land to hold back any rebellion.