http://www.mnn.com/earth-matters/animals/photos/natures-10-best-animal-dadsUnfortunately the message in the preceding is that being a good dad means being a good mom. Specialized parenting probably works a little better than androgynous parenting, at least in primates. The article mentioned pygmy marmosets, but probably a more common arrangement among primates is for mom to handle the newborns and dad to handle older offspring. A good mother nurtures; a good dad protects, trains, and encourages.
I didn't know about Rheas. I assumed they did the same thing as Ostriches, looking similar. Ostriches lay their eggs, then the parents get into rank-setting matches. The winners, alpha male and alpha female, raise the whole herd of chicks.
http://artofmanliness.com/2008/06/10/the-all-time-best-and-worst-tv-dads/