I am a big believer in CIO, but I just don't think CIO works for naps. If my kids would cry for 20-30 minutes at night at least they would sleep all night. But for a nap, it seemed like they spent as much time crying as they did sleeping and they were never refreshed from a nap that they cried for.
I am a big believer in routine though. If I were you I would establish a nap routine. He may not seem sleepy at the same time everyday, but his sleep patterns will adjust to the schedule in a few days or a week. I just learned this recently, but in the evening, if you keep a consistent bedtime, your blood pressure actually drops in expectation of sleep. If you keep a consistent bedtime it will be easier for you to go to sleep at that time every day. If your bedtime is inconsistent by more than an hour or so your body can't tell when it is time to go to sleep resulting in a tougher bedtime.
I know this is true for adults, but I don't think it is a big leap for kids. My kids nap at the same time everyday, and they usually don't fuss (my toddler fusses now, but he doesn't really need a nap anymore)
I feel like it can take about 3-5 months for a pattern in sleep to develop for a newborn. But you are right at the time when you can start guiding him to a good schedule. That is what your daycare will do for him. They can get a kid on a schedule in a week.
Of course there are exceptions to every rule. This too shall pass. Even if you did nothing it would probably get better on it's own because he is getting to be the right age for a consistent schedule.
Good Luck!