The campsite seems sort of random. I've had weeks with nobody on my campsite.
If you have any events coming up on that week, nobody will move out or request you to move out. Also, the "ignore villagers" thing may or may not work. It seems to be random which villager decides to move out, some people swear by ignoring them while other people say they've gotten pinged more often by villagers they've befriended. In my own experience, the villagers I ignore ask me less often to go.
Have you been TTing forward after denying someone's request to move out? If you say no, then TT on that very day, nobody will move in the time gap.
The way I get rid of villagers is pretty simple. I ask a villager to stay. Then I find a week with no events on it and TT to the beginning of that week. I save the game and quit. Then I use the 3DS calendar to TT one year ahead, start as a new character, and check if anyone is gone from the map Porter gives me. If so, I quit without saving, set the calendar back by one year again, load as my mayor and go find that character. If they don't ping me immediately I talk to them a few times, save and quit and load again, until they do ping me or say they're moving out. Then I save and quit, set the calendar ahead by one year, load as my mayor, save and quit, skip another year, use a new character to check the map, quit without saving, skip back by a year, use the mayor to talk to the missing villager, and so on. This tends to work well for me. I've had some villagers ping me multiple times that way and one of my villagers has never pinged me when I've used that method, but with some time and patience the one you want to get rid of will eventually ping. I find it easier than skipping random weeks ahead since that means I won't have to worry about events preventing them from pinging me.
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Oh, and your 10th villager can move out eventually. I don't know if you need to have moved in someone else before then or be down to 9, but a villager who was my 10th a while ago asked me to move out (I said no but she did ping me to ask, so it's possible).