S.B.
Ask and see what the parents say. If they say no...don't push. Some parents really aren't ready for their children to spend the night. Also, you MUST abide by the parents wishes. My inlaws had an overnight with my daughter when she was 1 (she is now 4) and that was the one and only time she was allowed to stay there. They completely disregarded feeding and sleeping schedules and even blatantly admitted they weren't listening when we told them what to do. They had even asked us to write it down and ignored it. When I came to pick my daughter up...she was so hungry and thirsty (scarily almost half the food we provided was untouched when it should have been almost all gone) that we decided they could not have her overnight again since they could not take care of her properly.
But even still, I am not ready for someone who I do trust to care for her to have her overnight and again, she's 4. I have a friend who has never allowed her son to spend the night anywhere else and he is 6. It's all about parents comfort levels. So all you can do is ask...but don't expect it.