Before I ever go into the tent to try and get someone to move in (9 or less villagers in town at that moment), I always fill all 16 spots with seashells and have 2 or 3 in my letters (doesn't matter how much money I have on me). Just keep talking to them until they agree to move in or they want to play a game to decide. If you lose, they will take a seashell but you can just pull another out of your letters and try again and again and again until they finally say "yes".
Good Luck everyone.
The fastest way to get a camper to move to your town is to go into the tent/igloo with absolutely nothing in your pockets or wallet.No bells,no tools,no furniture.......nothin'.The camper won't ask you to play any games and you can get down to the business of convincing them to move to your town.Just keep talking to them.It's never taken me more than ten or twelve minutes doing it this way.