If my son cut his foot open on a pipe on the side of the house that we rent and received stitches, is the landlord liable?

The landlord is liable for your son's injury because the landlord is the owner of the property.
You should contact the landlord and obtain his/her insurance information.
Notify the insurance carrier in writing that you will be filing a personal injury claim on behalf of your son.
When your son completes his 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 in his medical treatment where no further improvement is antiicpated, obtain his medical bills and medical reports I assume that your son is a minor and therefore there isn't any wage loss claim.  Your son's personal injury claim filed with the landlord's insurance carrier should include those items.
Compensation for the medical bills is straight reimbursement.  The medical reports will document the nature and extent of his injury and will be used to determine compensation for pain and suffering which is an amount in addition to the medical bills.  If applicable, compensation for wage loss is straight reimbursement.
If the case is settled with the landlord's insurance carrier, NO lawsuit is filed.
If you are dissatisfied with settlement offers from the landlord's insurance carrier, reject the settlement offers and file a lawsuit based on premises liability against the landlord.
If your son is a minor, you will need to be appointed guardian ad litem to file a lawsuit on behalf of your son because a minor cannot file a lawsuit himself.
If the case is NOT settled with the landlord's insurance carrier, the lawsuit on behalf of your son must be filed prior to the expiration of the applicable statute of limitations or your son will lose his rights forever in the matter.