Is it alright to give an 8mo infant tylenol (acetaminophen) syrup just once a day at nighttime for teething pain and crankiness? For how many days can it be given?

Try teething rings. One appropriate dose of Tylenol (acetaminophen) a day is probably not going to cause any harm, but you do not want to get the child used to taking an oral medication when it may not be needed. Try teething rings.