We just started this too and I thought I was going to cry without his nap! I didn't realize how much we needed that "downtime".
Our little guy will nap at daycare, but on the weekends he just wants to be with us, so now that he doesn't always "need" a nap, he has decided that he won't take one! I got some great advice from a neighbor and it actually worked:
1. Take "noisy" or "physical" toys out of the bedroom so that the bedroom is for sleeping and quiet play time. Load up on books (from the library), puzzles and stuffed animals.
2. Every day at whatever time, announce "it's rest time" and (at least in the first week or so), make that apply to everyone.
3. Kiddos off to their rooms for "quiet play"- be specific... books, puzzles or cuddling. My son likes to have his music on so we taught him how to do that himself and preset the volume and station to classical.
4. Everyone is quiet during "rest time"... including the adults (until the kids are into the routine). Read a book, magazine, pay bills, do your nails- whatever- as long as it is quiet and mirrors your expectation of them.
There was a lot of "it's rest time, you need to go into your room" for the first two weeks and it was not restful for any of us, but now he's pretty into it. We go to the library every week so his book collection rotates.
We do 30-45 minutes at the most. Good luck!