Legal Question in Personal Injury in Georgia

Are the board members individually liable? Highly unlikely. Where are the parents or sitters, who had the last opportunity to see the equipment? Beyond that, obviously you chose to not tell us how the child was hurt so no one here can tell you if anyone was liable. Children get hurt when they play. They almost always recover.

Since you gave us no details we can't answer, but I am sure the HOA board immediately reported it to their insurer, who will defend any claims.

Unlikely the board members themselves are liable. The HOA might be. But you didn't supply us with enough facts to determine that.