Yes definitely include your cleaning jobs. How you were paid is irrelevant for these purposes, it's the responsible, reliable attitude it conveys that's important. Will one or more of your previous employers be happy to give you a reference?
Have you volunteered at a nursery or been some kind of parent helper at a school or anything similar? Stuff like that would be good I imagine.
Other than that I expect you need to be cheerful, outgoing, patient, friendly - that kind of thing.
Think through the list of the qualities they want in the person - friendly, able to cope with stuff - and try to include things in the form that show you have those qualities. So, you're good with children, hardworking, helpful... whatever it is they want! But think of ways to show you actually are, not just saying it.