Normally it takes a couple of tries to convince them to move to your town; you will never get it on the first try.
Also, campers take longer to plot in your town, normally 2 days. However, there may be a possibility that they'll take longer.
Sometimes it can take ages for villagers to agree to move in, what I did is I keep refusing to play games with them until they agree to move in. It takes ages but it's worth it, i'd also recommend dropping any important items outside of the campsite.