Barnes hasDown Syndrome.
The family gave the YMCA until Nov. 15 to allow Jonathan in their after-school program in Lee County.
The YMCA agreed to let him come only if his parents hired and paid for a staff member to be with him at all times.
Barnes' family say that solution is unacceptable, and their next stop is federal court.
"It's like they're telling my son he's not good enough. He's not as good as the other children. You look a little different. We only want normal, whatever that is, normal children in our program," said Sylvia Womble, Barnes' mother.
In response, the YMCA says: "Over the years, the YMCA has served tens of thousands of people in this part of North Carolina including children and adults with special needs. Every special situation is evaluated carefully on a case-by-case basis."
The family plans to sue the YMCA for discrimination under the "Americans With Disabilities Act."
"It's our position that they could accommodate Jonathan fairly easily, and it would not create any significant burden for the Y. Why they are not doing so, I really don't understand," said attorney Charles Putterman.
"By looking at Jonathan, they made some determinations and some decisions, rather than looking at the individual and giving the child a chance," said child advocate Ellen Russell.
Once the lawsuit is filed in federal court this week, the YMCA will have 20 days to respond to the allegations.
Barnes' parents say he has been in other after-school programs for at least five years without any problems.