Oh lord. A 4 month old really shouldn't be already taught to watch screens. They're not hard to entertain, believe me. You could do practically anything and just hold onto the baby. Hey, get a book. Even if the child doesn't know what's going on, it won't with the app either, so it's better to go with a book. Music, a nap, a movie could be okay, but what better way to start a kid off than with words and puzzles?
Im not sure about app's , they should have a childrens section although remember that all that matters is colors and sounds since they have a short attention span and wont understand whats going on. We used to go to cv (cingular vision) or the disney channel website from our phone and play episodes of mickey or whinne the pooh.