The main risks of Coumadin are GI bleeds, excessive bleeding from wounds and higher risk of spontaneous or traumatic intracerebral or subdural hemorrhages. For young people with no brain atrophy, spontaneous intracranial bleeding is uncommon, and GI bleeding has nothing to do with scuba.
Thus, the chief things to avoid are head trauma and lacerations, neither common in scuba, I would presume. Penetration wreck diving might carry some risk of being cut, but that's about it. If a diver is cautious, taking care not to fall on slippery, heaving boat decks, staying away from jagged wrecks, watching so the tank doesn't slam you in the occiput during the giant stride, I don't see a problem.
This isn't to be taken as advice in lieu of consulting your personal physician. Given your age, I presume you take Coumadin for a valve replacement and so may need a higher INR than someone taking it for phlebitis or vascular disease. Does your INR run high and how often is it checked???