Well, as if you wanted it or not, here is my take on it, from my own experience this last year.
My father was never a religious person, almost pushing into agnostic/atheist territory for most of his life. He was then diagnosed with Lou Gehrig's Disease. Out of curiosity, after he had been diagnosed, I asked him what his belief system was, and he said he beleived in Christ and beleived that though his life was going to be cut way too short, ( he was only 52 years old at death, and had just retired after working for the state for 30 years, january 31st of last year), that his die was cast in stone. I told my the rest of my family his beliefs, and most were relieved. Part of my family is ultra-religious (for lack of better term), and had priests etc. etc. coming up to the house. One priest asked if he was a tire kicker and in ways (from what I took) was trying to say my father was bluffing. Then my Dad started getting e-mail's from cousin's and such about how they found god, but yet, he allready explained he beleived. Dad got very sore and irritated with it, to the point where he said he would have no talk anymore of it, what was said was allready said. My Dad swore up and down from the day he was diagnosed he could see angel's that would try to help as best as they could.
I know this is different in ways, in that your uncle is still a buddhist and is dying, but, I'm trying to bring up the key notes of trying not to push your uncle so hard. Ask him politely, at that, and if still no go, you have to let him be. You may think the bible tells you different, but in the end you have to respect the last few days of his life and let his belief's take him where his belief's take him. Who's not to say that he gets what he wants out of it? Sure, I don't know what he may get, but nor do you. You may think you can say for sure, but you really can't, and that's not to knock on your system either. Let him be.
Take care, and prayers go out to you and yours.