What are some good over-the-counter child medications for runny noses?

Allergies. If your child has allergies (sneezing, itchy nose, itchy eyes, runny nose) then try zyrtec (cetirizine), claritin/alavert (loratadine), Allegra (fexofenadine) or Benadryl (diphenhydramine). If he/she has a cold with runny nose no cold meds are recommended under age 6. After age 6 there are lots of choices. They help a little (not a lot). Common brands include triaminic and dimetapp.
None. If you just want to have something to do, opt for spending more quality time with your kid. None of these products have much to offer in small kids, and most have antihistamines that thicken mucous and sedate the kid.