I have a friend that would like to take his kid out small game hunting and was wondering if his kid can use a pellet gun to take game.

His kid is not old enough to take hunters safety, but can he still hunt under the direct supervision of his father?

Not sure where the pellet gun falls in for legality, but yes, the kid can hunt with his dad-as in, dad has to be close enough to make sure he's being safe. Taking my daughter out in a couple weeks for youth deer season. For us, her gun will be the only one, and I did confirm with DNR there is no minimum age for the tag.

I'd call a DNR officer in your county and ask about the pellet gun. Based on my experience with vermin though, he'll be better off with a .22 or .410. With vermin you don't care if they get away. Game, you want to eat or stuff it, so you don't want to lose it.

Father needs to have a hunting license, kid needs to be under 16.  Kids between the age of 12-15 can hunt unsupervised if they have passed the hunters safety course and have a valid license.

I did not see anything specific about pellet guns in the reg's.  I'm assuming we are talking about rabbit or squirrel hunting.  I would not see a problem if you take range and accuracy into consideration.  High quality pellet guns have no problems taking small critters if the shooter does their job, but I wouldn't recommend a cheap Crossman.  A decent .22 would be a better choice overall.  Best thing for him to do is contact the county DNR officer with questions.

PDF of the DNR reg's is at this link:  https://www.iowadnr.gov/hunting/hunting-licenses-laws

He should sit down with his kid and review the reg's, it will be a good primer before they take the hunting safety class when they get older.