As Greg said, any of the SA series Mossbergs are good choices, and I also have the Mossberg Youth Super Bantam which has not disappointed me in any way the past three years I have carried it. Gun weighs 5.25 pounds naked out of the box and is a joy to carry.
All that said, Remington is back guys and I think they are building as good of an 870 as they have built. If a 20 gauge is not too much for your kid, I would spring for the Remington 870 Youth Fieldmaster in synthetic hardware. Gun is only 40.5 inches long. It is a hair heavier than the Mossberg Youth Super Bantam I mentioned above, but you have a solid steel receiver and heavier twin bars on the slide. I just got this one back from having it cerakoted, and have attached a Leupold Delta Point Pro on it - and cannot wait to kill a turkey with it.