I'd start with
Dennou Coil, a science-fiction story about ten-year-olds who live and play in a virtual world that's overlaid onto their small japanese city. Great mix of comedy and drama, beautiful animation, and one of my favorite scores of all time.
As others observed, many anime for younger viewers target girls; indeed the "plucky girl" genre of show is one of my favorites. Some of these, like
Noein, are probably too complex for his age, but others should be fairly accessible.
Angelic Layer - kids participate in a contest where they fight arena battles using mind-controlled dolls
Nijuu Mensou no Musume - a young heiress has adventures with a master thief; people die in this show, though, and some of those deaths might be disturbing
Rocket Girls - cute show with lots of real science but a silly premise; commercial Japanese company trying to launch space rockets decides to use teen-aged girls because they weigh less than adult astronauts; the main girl's parents are both losers
Shows with young male protagonists
Seirei no Moribito - an adventure set in a fantasy Asian land (~ T'ang China) where a 30-ish female bodyguard is tasked with protecting a young prince; designed for a family audience from a light novel for children; some fighting and a bit of gore, but less so than, say,
Mononoke Hime
Hikaru no Go - a young boy encounters the spirit of a Heian-period Go master and becomes inspired to take up the game competitively; more compelling drama over a board game than you could possibly imagine
Another big thumbs up for
Chi's Sweet Home. If you happen to own a cat, as I do, you must see this show, but nearly anybody would think it's cute and funny. Episodes are only three minutes long.
Shows that might work, but one's that you should preview for content:
Allison to Lillia (?) - I wasn't a big fan of this show because I thought it too childish; might be good for a six-year-old though
Hakaba Kitaro - dark, but comedic show about a young boy who is the "last survivor of the Ghost tribe"
Ghost Hound - kids discover they have the power of astral projection and use it to investigate strange happenings in their rural Japanese town; may be too "heady" with its use of psychology and brain science; implied adultery and dysfunctional families
Jungle wa Itsumo Hale nochi Guu - strange girl Guu joins young boy Hale's family living in a technicolor jungle; very funny, however Hale is illegitimate, and his mother drinks heavily
School Rumble - wacky comedy about high-school romances; while the issues in
SR are in his future, the offbeat characters could be a hit
Natsume Yuujinchou - a teen-aged boy becomes a source of comfort and aid to lonely monsters; might be too slow and too much "slice-of-life" for a young boy
Shouldn't this be in the Suggestions forum?