First off, be consistent. It doesn't sound like he's crying just playing so what I'd do is pick a wake up time, nap time and nap over time, and bed time. So if he goes to sleep at 7:30 p.m. (just an example), I wouldn't get him until 6:30 a.m. Then nap time is 12:00 p.m. and supposed to be 2 hours so I wouldn't get him until 2:00 (again as long as he's not crying). Then bedtime again is 7:30. Just be consistent. Do your routine, shut the door and that's it. Don't go back in until 6:30 a.m. in the morning and 2:00 for the end of nap.
The way to deal with a stubborn toddler is not to. They will get used to you being gone and learn that your not going to play his game, so he has to either sleep or not sleep.
Someone on this board gave me GREAT advice. They said you can provide the time for her to sleep, but you can't MAKE her sleep. That is so so so true. And that's what I do. She'll play, sing, read, etc., but she knows Mommy's not coming until nap time is over. 90% of the time she falls asleep within 15 mins now.