I agree with Adam Serwer on this:
Mammy" is not a "positive" stereotype. There are no "positive" stereotypes, all stereotypes are created with a dehumanizing flip side that is inseparable from the faint "compliment" used to justify their invocation. But the legacy of the Mammy in particular is a grotesque one. Like every other carefully engineered old-school caricature of black people, it's meant to reinforce notions of what kind of behavior is appropriate--in this case, a docile, even happy acquiescence to white authority. "Mammy" was meant to depict black women as ugly and asexual, content to exist as surrogate mothers to the saintly white children of their owners or employers. Mammy's false happiness assures white people that the institutions of slavery and later Jim Crow have black people's consent and approval, her rotund body an alibi for the rampant exploitation of black women by their white slave masters.
There's simply nothing "positive" about it. Mammy may give some people the warm fuzzies, but that has to do with whom the stereotype flatters. It sure as hell doesn't flatter black women.