Coyotes | Animal Rights Foundation of Florida I found this link. That is true that the displaced coyotes in the south part of the Villages would probably soon take the place of any trapped on a private residence. The same logic though applies to coyotes endangering protected species in the wildlife preserves unless the VCCs hired a lot of trappers or a couple with very long contracts.
I do see the liability problem except for traps set on golf courses from midnight though 4AM or so. They could also announce the setting of traps at these periods so that almost no one would be on these golf courses in the middle of the night. That does seem to be how the coyotes are getting around. There would be the problem of loose dogs or feral cats getting into the traps but that would also apply to the protected preserves as well.