Label recommendations for borax poisoning say to treat the symptoms. No cure.
Potential Symptoms:
Nausea, Vomiting, Diarrhea, Pain, Rash around areas of contact (throat), difficulty breathing and possibly death. If he survives he may be infertile.
I would try to give him roughage (greens) if he will eat it. Just to try to get more of the boron to move out of his system rather than being absorbed. Get him to drink lots of fluids to counteract the diarrhea and the yogurt would be good for the rash. Keep him in an area with good air flow and if he starts convulsing try to keep his airways clear.
Even though label recommendations don't say there is a cure, I might try feeding him some human grade activated charcoal (charcoal can bind to some poisons and carry them out of the body. I don't know for sure that it will work with borax, but it's worth a try.)