Time magazine has two lists of apps, ostensibly, for new parents.
The first is "Seven iPhone Apps for New Moms" which includes such useful (for an iPhone app) things like Nursing Tracker (a sort of diary of nursing), some white noise apps to help babies sleep and Toddler Cards (electronic flip cards to help with learning). You can see the full list here.
For Dad however, the list (which includes three extra apps for a total of ten) NOT ONE of them has anything to do with being a father, helping raise a child or do anything other live the life of a bachelor. We get carpentry apps, booze apps, sports bar apps and exercise apps. The only one that even mentions 'family' is an app for the incredibly unfunny Family Guy television show. The full list is here.
I guess the vaguely named "Things" app could be put to some sort of fathering-based use, but it's nothing more than an electronic to-do list. But for $9.99 you're better off using the calendar and notes apps that come standard.
Shame that Time couldn't find, out of thousands of apps available, one single app geared towards men hoping to raise a child in a healthy equal relationship with their partner.