Harry Studley remains in a critical condition in Bristol Children's Hospital after being shot on Friday.
Jordan Walters, 24, and Emma Jane Horseman, 23, of Bishport Avenue, have been charged with causing grievous bodily harm.
They have been remanded in custody to appear before Bristol Magistrates' Court on Monday.
Police were called to a flat in Bishport Avenue in Hartcliffe at about 16:10 BST.
Harry's parents, Amy Allen and Edward Studley, said in a statement issued through the police: "We would like to thank everyone for their continuing support at this time.
"Harry is still very poorly and we would reiterate that our request for privacy be respected as we and our family come to terms with what has happened."
They said they were "concentrating our focus on our son Harry's recovery".
Two people have been charged after a one-year-old boy was shot in the head with an air rifle in Bristol.