Most of them don't have a nursery. We've been regularly cruising with
RCCL for over a decade, and we've never been on a ship with a nursery. We have cruised when both kids were under 3, 4 or 5 times. We have been on many of the older ships, but we have not been on the big, new ships, which I understand do have nurseries. So, yes, a few of the ships do have, like Disney, the pay for it nursery, but you have to check on a ship by ship basis.
What they do have is Royal Babies/Royal Tots, a Mommy(or Daddy) and me program, which they used to partner with Fisher Price, but now do on their own. You go to a playgroup with your appropriate aged child. On one of the cruises we were lucky and there weren't many preteens, so they left that area set up with toys for toddlers so that you could go in and play there (unsupervised) throughout the day.
Maybe they've gotten better with the under 3s in the last year or so. I heard they were trying to improve under 3 offerings, but they were pretty disappointing for many years. Don't get me wrong, we still had great cruises when we cruised with our kids, but the ships themselves didn't have much to entertain the little ones. That is one area
DCL did much much better, and one of the big reasons we switched to DCL for the last couple of years.