Is it permissible for a Muslim to ask a non-Muslim to supplicate for him, and are there any Hadiths that indicate this?

It is not permissible to ask a disbeliever (kafir) to supplicate [for you], because he is not worthy of having his supplication answered, and he is abhorred by Allah. Also, requesting this implies exalting him and assuming goodness in him despite his disbelief. Rather, supplication should only be requested from believers. A disbeliever's supplication might be answered as a form of enticement (istidraj), but saying 'Ameen' to his supplication is forbidden if it suggests exalting him.