I actually went through that exact same scenario when I offered to watch my neighbor's daughter (she was 4 months old at the time). They knew she was difficult, but I thought with some regularity and time and the right approach, their daughter would "learn" to go to sleep more easily. Part of my issue was that the parents kept a different schedule on the weekend than what I did at my house despite their buy-in and my efforts to get them to be consistent with our plan. That was the biggest factor - inconsistency. Also, she was used to much more hand-holding, coddling, someone laying with her to go to sleep, etc. than I would or could do given that I had 3 kids of my own to care for. I thought that after a couple of weeks it would straighten itself out, but it didn't. I even approached the parents about checking to make sure there wasn't any health issues (like one of the other mother's suggested). After a 4 weeks of no change (and little help from the parents), I decided it wasn't working out for me, their daughter, and my family, so I gave them notice to find another day care provider. The parents weren't happy about it, but in the end, they found a daycare provider that worked well for them and their daughter, and I was no longer a frazzled (more than usual, anyway) mom to my own family.
I agree with Jeanette P that you should first try to work on the arrangement with the parents, but if you've made attempts to work on it (with or without the parents' help) and the situation does not change, do yourself, the baby, and the parents a favor and request they find another nanny or daycare provider. It may be tough call to make if you have to, but you'll be glad you did.