When you say you have slots open I'm assuming you mean you don't have the max amount of villagers already in your town, right ? If that's what you mean then just keep at it is the best advice I can give you lol, some campers will say yes right away but others may take a loong time, it's happened to me but they eventually agreed after a game of charades
I've heard that going into the tent (or igloo at this time of year) with no bells or items that they might want to buy off of you can expedite the process but I've never tried that so idk about that for sure..
Either way good luck !!!