I wouldn't recommend sharing a UA C seat with an infant.
There are exceptions.
- 747 upstairs works great, since there is enough room to put a baby down next to the window.
- 747 first class is fantastic if you can get the front two seats. There is enough space to put a baby travel crib on the floor between the seats.
Or fly an airline that doesn't upgrade as happily as UA. Our baby got his own business class seat on LX both NYC-ZRH and ZRH-SIN.