Run! Run for your life! Nah..... Seeing one coyote crossing the field doesn't mean they are starting to become a problem. Just consider yourself luckey.
Have the local farmers been having an issue with smaller livestock getting eaten?
Do you have a season in N.C. for coyotes? If so hunting them with calls can be really fun.
Unfortunatly, I'm no expert but I'm pretty sure they have 1 - 2 litters of pups per year. That's doesn't amount to very many pups per female with the mortality rate. Someone here probably can answer that question a lot better than me.
Another good place to post this question would be in the 'Small Game, Predator and Trapping' Forum. There are a good bit of coyote hunters that frequent that part of the msg board.