D.P.
It's a sad day when the nap goes South! My son started resisting napping at about age 3 too. What I started doing was letting him choose a DVD movie to watch in his room. That would be good for at least 90 minutes of quiet time. Sometimes he wouldn't actually stay laying on his bed, but if he got up, he would stay in his room, playing with cars, animals, etc. on the floor in his room at least til the movie was over.....good luck!