I am so sorry you are facing this with your dear dog.
I really don't know about Benadryl. So I can't advise about that. But my own fear (if it were me in your position) would be getting it wrong and making things much worse. If for instance it caused vomiting while your dog was half unconscious, he would choke to death in the most awful way, and might feel it.
If someone else replies -perhaps with some medical knowledge or experience -and says that they know it is safe, then that's different.
But my own feeling is please do try to get him to a vet to do this. Euthanasia is not an expensive procedure, compared to many vets bills. Could the money for this be borrowed from someone? Or from a bank overdraft? To be paid back in stages perhaps?
I am so sorry. My kindest thoughts to you at this hard time, and to your beloved dog.