OK... so this is highly contraversial, and I'm going to get flamed, but...
My DD would never sleep on her back. Not in her moses basket, cot, in our bed, nowhere.
After a few weeks of agonising about it, we gave in put her down on her tummy and never looked back.
We were VERY careful about all the other SIDs risk factors, and bought a movement monitor, so if she did stop breathing we'd know within 20 seconds.
If I have another, I will certainly try and put him/her down on their backs, but I feel that, for whatever reason, some babies just hate it.
A half way house might be to try her on her side, propped with rolled up towels or whatever.
I'm not advocating anything, just telling what happened to us. Maybe we should have persevered and she would have got the hang of it eventually, but after several weeks of no sleep we just gave up. We spoke to the Doctor about it, and he said 'Well if she won't sleep on her back, then you have no choice do you. Just be very careful and keep a close eye on her.' Or something along those lines.
She's 14 months now and still hates sleeping on her back - as do I, funnily enough.
[Ducks behind sofa...]
db
xx