Can I give my 4 year old melatonin and allergy medicine (zyrtec (cetirizine)) in the same day? If yes what would be the proper dose of melatonin?

Yes, but why?? There are no bad interactions between zyrtec (cetirizine) and melatonin. They are safe to use together. The bigger question is why daily melatonin. I imagine it has to do with poor sleep initiation patterns, but without knowing more, i would talk to his pediatrician about its use. A usual safe dose for a 4 y/o is 3 or 5 mg at bedtime, but as important is bedtime routine, decreased stimulation, etc.