Hmmmm mine can be a bit of a bugger during day sleeps as well. Does she sleep on you? Is that how she can fall asleep? Sometimes if Ryan (8 weeks) will not sleep in his cot, I just deal with it and let him sleep on me because I'd rather him get some sleep than none at all.
Does she have a nice full belly before putting her down? Have you tried wrapping her or using a dummy?
At the moment, Ryan is in his cot whinging a bit, but he is SO tired. If I go to get him, he will fall asleep in my arms, so I will put him back down and he will whinge again. Sometimes it is hit and miss whether he wants to sleep or not.
I guess you just have to persist with settling, wrapping, dummy...try anything and everything and eventually you will find something that works.
Good luck, but remember you are not alone