Great suggestions by Deanna Leigh.
Your son has been very good about "quiet time"... but as with any child, each day will be different. On some days, even though they try their best... they may still not be able to fall asleep etc. or be subdued.
I have two kids, and they still nap, everyday, or my eldest has quiet time.
My daughter is 6 yrs. old and still naps in the afternoon about 80% of the time. She is simply tired by the afternoon time & after school, but with her, and per her maturity... I let her have quiet time if she does not or cannot fall asleep.
For me, what I do for "quiet time"... is I tell her she must stay in her room, and she can do quiet things of her choosing. And also, because her brother is napping too, she needs to keep quiet or he will wake up. This is the "rule."
I also tell her that "It's Mommy's quiet time too... so, no chatting, playing loudly etc." and I tell her (in order to coax her), that this is not play-time with Mommy time either.... It's nap or quiet time, ONLY. AND, no turning on of anything electronic, including any lights. So, that is enough of an incentive for her. And she does cooperate. Then I also tell her that it's Mommy's "work time..." or I pick up and read a magazine.. .and that's it. Then she goes in her room. I am right nearby in visual distance. If she tries to chat or whatever, I just keep repeating "nap time..."
The thing is, we have made it a DAILY ROUTINE EVERYDAY... and so both my kids are used to it, and they don't protest about it, and they will even get ready for "nap" in the afternoon. Or, for "quiet time."
Yes, to me, I believe quiet time or down-time is important... or the child gets too exhausted or over-tired and then major fussy. At least in the case of my kids. So, EVERY afternoon, at the same time, I put both my kids to nap... or my daughter has the option of "quiet time." But I will first have her "try" and nap... then if she can't she is allowed to have her quiet time IN HER ROOM.
My son, who is 28 months old, is napping now in fact, and my daughter is getting ready for her "rest" time.
It just takes consistency... and regularity. But, there will be good days and not so good days. It's all normal and it's okay. But, just keep to your regular routines. And the child will slip into that "routine" too... like any "habit." But give it time, and don't expect perfection everyday.
But for me and the kids, every afternoon is this "quiet" time or nap time. But, I NEVER punish them for it, if they can't nap. I allow for divergences, if it occurs. Nor do I use incentive charts or 'treats' etc. I just do it, as a "rule." And my Hubby resonates/reinforces the same "habit" in them verbally as well, when he is home.
And yes, many times a child will SEEM like they don't "need" naps anymore, but if given the chance, they will go back to napping as Deanna Leigh mentioned. At certain ages, they will ebb and flow about napping. But then get back on track. Both my kids went through this too...but they still nap and I still have our "routine."
Each child is different... but this is just what I have done, and has worked well with my kids.
*oh just read you are having a baby soon! Yes, STILL KEEP to the same routine for your son, as much as possible. In the long run, this will help immensely! That is what I did with my eldest, when I had my second baby.
All the best,
Susan