As I said, there's the Math League. There is also MOEMS (Math Olympiads for Elementary and Middle Schools) which I would rank third under the AMC and MATHCOUNTS, but you are looking for individual competitions and MOEMS only takes teams (though homeschool and institute teams can compete as well as school teams). If you look at Rusczyk's Problem Solving books; these are the competitions he pulls problems from. He also includes 24 cards, and you may find some local 24 contests that are open to individuals. The top four contests open to students in 8th grade and below, in my opinion, are the AMC 8, MATHCOUNTS, MOEMS, and the Math League. After those, you should choose any competition you think your child would enjoy or excel at, keeping in mind most won't challenge students who are really strong in mathematics.