If I am a landlord and my lease agreement states no pets inside or out but a the tenant had a Pitbull on the premises that attacked a child, can I be liable?

As the owner of the property, you are liable for the child's injuries despite the provision in your lease prohibiting pets.  Your liability would include the child's medical bills and compensation for pain and suffering.  Compensation for the medical bills is straight reimbursement.  Compensation for pain and suffering is an amount in addition to the medical bills.

The child's parents could file a personal injury claim on behalf of the child with your property insurance carrier.  It would be premature for them to file a claim until the child completes medical treatment and is released by the doctor or is declared by the doctor to be permanent and stationary which means having reached a point where no further improvement is anticipated.  If the case is settled with your insurance carrier, NO lawsuit is filed.  If the case is NOT settled with your insurance carrier and a lawsuit is filed against you, your insurance carrier will provide you with an attorney at no cost to you.  Your insurance carrier will handle the case for you.  If there is a judgment against you, you could sue the tenant who owned the dog to try to recover the amount of the judgment against you.