First, you should check with your pediatrician to be sure your child is truly allergic. Many people who think they're allergic to antibiotics just tend to have severe side effects. A true allergic reaction would include symptoms like swelling of the lips, tongue, or face, hives, or wheezing; in severe cases it could also trigger anaphylaxis, a multisymptom reaction that can be life-threatening. Although there's no definitive test for all types of drugs (there are simply too many), an allergist can perform skin tests to check for allergies to other antibiotics, as well as more common childhood medications like Novocain and other local anesthetics.
Since it's difficult to narrow down every drug your child could possibly be allergic to, your first line of defense should be to keep a list of all the antibiotics your child has had reactions to, since there may be other similar drugs that should be avoided as well. For example, many kids who are allergic to penicillin also react badly to other antibiotics like amoxicillin and ampicillin (which come from the same family) as well as cephalosporins (another family of antibiotics similar to penicillin). So if the doctor knows your child is allergic to one of these, he'll avoid prescribing all of them.
And should a doctor ever prescribe antibiotics, discuss your kid's allergy with him and be sure the meds are absolutely necessary, and whether an appropriate alternate antibiotic should be prescribed. If they are, then watch your child very closely and be prepared to treat a reaction. This usually involves stopping the drug immediately when symptoms appear and taking an over-the-counter antihistamine like Benadryl. A more severe reaction may require oral or injected steroids. If, at any point, you suspect anaphylaxis (symptoms include dizziness, wheezing, pale skin, vomiting, and a weak, rapid pulse) go right to the ER.