Hi A.,
I had the same exact problem with my little girl starting at around 3 months of age. She would not let me lay her down to take a nap she would sleep on me just fine. I tried the cry it out thing but since she is my first child I had a really hard time doing that because she would scream for hours. One day I tried for four hours to get her down for a nap and she slept for a total of 30 min.
I finally started letting her sleep on me to get her to nap. I wished I would have known about the book "Good night Sleep Tight" It would have helped a lot. It is a great book. I just bought the book not to long ago because I am still having issues with my child sleeping, but she is taking regular naps now in her own room and bed. She is 15 months old. We are now working on sleeping through the night.
My advice is to keep trying different things but definately try to get her trained early before she gets the age of my child because I wished I would have found help a little sooner then I might not have had the battles that I have now especially since she is running around. Hang in there.
Also I used to put my child in a saucer first then when she was a little older a walker and carted her from room to room with me to get things done. Now that she is mobile she has started playing on her own and even goes into her room to play by herself. Hope some of this helped.