dougk - sorry to hear about that. It is very disappointing when the first round doesn't stop the animal's pain. I have witnessed that same scenario a number of times on the NYS Thruway - the worst of it is that you have to wait for the State Police to come and finish the job (especially if there is someone around to get your license plate number) and they are simply not in any great hurry to get there and they are lousy shots.
As jhm indicated, the 9mm will do the job, but I have seen a number of different calibers fail at this task. I have some field analysis of wound channels on harvested game and have found that in some instances where head shots were used to euthanize the animal, round nose bullets, soft nosed bullets and some hollowpoints (not all from autos)may impact the skull but flatten and travel along the bone beneath the hide, exiting the hide beneath the jaw. This gives you the idea that the bullet has penetrated clean through, when it hasn't. This has happened to a couple of State Troopers - they thought the animal was 'done' (snap a tap from the Glock and she's done) after just one round and got miffed when we would have to yell for them to come back and finish the job, and it was never pretty.
I feel the best bullet you can use for that job is a semiwadcutter and the best place to put the round is right down through the top of the head where the skull is flattest. Trying to place it through the back of the skull may often get you a deflection due, in part to the shape of the skull and in part to the shape of the nose of the bullet. Failing a top down shot, which is often difficult on a thrashing animal, placing the shot through either side of the skull halfway twixt the eye and the ear is as effective as a top down shot. If you can get a straight on shot at either of the flat spots on a whitetail's skull most 9mm bullets should work for you. I know a few fellas who carry spare rounds or spare mags for just such situations.
Again, sorry to hear about that situation but am glad there was a man around to help ease that animal's pain. JMO. Mikey.