We don't cosleep anymore, but when we started making the transition it took us awhile to get naps right!! A few things I found helpful initially were white noise machines, and good light-blocking drapes. Her room is dark, comfy, and we have the gentle giraffe. Sometimes we use our iPods as well.
One thing that we still do at 16 months is rocking DD to sleep- completely, totally, zonked out asleep before we put her down. Then we just ease her into the bed. We never got down with the "drowsy but still awake". If she wakes up, we stay in the room with her, but leave her in her crib.
We usually lay on the floor by her crib & pretend to be asleep ourselves, and she'll play a bit, then lay down & go back to sleep. At first, she would call to me, so I would calmly talk to her & explain, "this is nap/bedtime, and we need to rest now. So Mommy's going to lay here, and you can lay in your bed. Good Night." Sometimes we'd sing to her, or give her a little toy to play with. It doesn't always work- but with some practice you can find what works for you! I know some mommas just put their heads down on the side of the crib, or sit back in the rocker, so baby knows they're not alone.
Now she happily sleeps in her crib & seems to prefer it to our old cosleeping routine- and we still rock her every nap & every bed time.
If she's in daycare though, I might be curious what they're doing to put her down for a nap while she's there- because perhaps the environment is different & that's why she's struggling at home?