DD2 often had probs sleeping lying down. She had reflux and often had a bunged up nose too. I think the reflux can cause tummy pain and the stuffy nose meant she couldn't breath. So sleeping lying down was more than she could bear.

In your situation, I'd try holding her to sleep then transferring her to her pram (in upright position). Sit next to her just before she's about to wake up and see if she stirs see if you can pat her back to sleep.