No Naps. - De Pere,WI

Both of my kids gave us napping before their little bodies were ready. As you know, you can't make them sleep.
Quiet time also never really did much for my kids.

I still have the "no nap monster" on occasion. But my tactic when it kicked in was to get them out of the house and distracted as much as possible.
Something as simple as going to the store was enough to shift the routine and kick them out of that mode. Playing outside, recycled toy (and old one they haven't seen in awhile), etc...
Something that causes a distraction.

I went through this with my youngest, a boy.
He was almost ready to give up a nap but not quite as he would fall asleep way too late in the day then it was a late bedtime.
He would be cranky w/o a nap though.
This phase lasted about 6 mos.
The best thing I could do was run an errand in the afternoon. He'd fall
asleep in the car. I'd either wait in whatever parking lot of the store I
needed to go into for 30 mins or immediately drive home & stay in the
car w/him for 30-60 mins while he napped in our driveway. I'd keep a
book in the car & that would be my quiet/me time.
It didn't last long as a phase, he still got the nap he desperately needed &
I did what I needed to do to work w/i those parameters.

While this wasn't overly successful with my kiddo (he was done with naps, and nothing I could do was going to change that) for awhile he would do "rest time" where he got to pick a basket of quiet toys or books to play with/read in bed. Then I would turn on some quiet music, and he had to stay in or on his bed until the music stopped (about an hour). Some days he'd fall asleep, some days he wouldn't, but either way he had some down time, and so did I!

If my kids fell asleep in the van on the way home from our afternoon outing I left them in the van to finish their naps. If it was hot or cold I pulled the van into the garage, if it was nice out I left it in the driveway and found something to do where I could see/hear them if they woke up.

I'd drive to the library and let them have a "get the edge off nap" when I thought their mood needed it. Otherwise, we do 1-2 hours of quiet "video time." It's like sleeping but without the mess (my oldest would trash her room during quiet time, so I decided, after having my second, that the Tv was in fact my friend.)

For what it's worth, my two oldest gave up naps at 2. And my second is/was an amazing sleeper.

my son swore off naps by about age 4, he was just too busy! He did get cranky-tired by the end of the day, so that led to earlier bedtimes for a while. I might recommend backing up his bedtime on those days that he skips his nap? I didn't really run into the no-nap monster at that hour; for my son it was later.

When my kids gave up their nap, I don't remember the "no nap monster" lasting more than a week. It wasn't a particularly fun week, but it did pass.

Honestly, it can't hurt to use the tv a little bit while you're getting through this phase. Maybe put on a cartoon while you're making dinner. Be sure to do bath time and books to help him wind down before bed, as an overtired kid is a bear to get to bed at night.

Good luck! It really does pass. I honestly think life is so much easier once they stop napping. No more rushing home in the middle of the day for naptime. You can relax and be spontaneous.

Our son napped till he was 7 yrs old.
In kindergarten they had nap/quiet time and his teachers were surprised at how heavily he slept - but they also said it looked like he was taller after his nap - it was almost like watching him grow before their eyes! (that was the first year he shot up 4 inches).
In first grade there were no more naps at school (boy was he cranky by the end of the day) but he napped on weekends.

He was always afraid he'd be missing something so we all laid down with him on our bed - the plan was as soon as he was asleep we'd get up - but more often than not we'd ALL end up taking a nap.
I usually got up first and I have some cute pictures of him and Daddy napping together!

Have you given any thought to trying a "quiet hour" for him?
It worked for us.
My son would be in his room, on his bed, books or quiet toys, or watch a 60 minute movie or DVD...or music.
I made it clear he didn't have to sleep--just play quietly or rest for an hour.
I think I needed that hour more than he did some days! Lol
And on the days where quiet hour didn't happen? Early bedtime!