I love how it's over a year later and there are still some relatively new replies to this.

My two cents:
Unless you can provide definite proof that the person in question is either dead, or YOU, they will not provide you with a certificate due to privacy regulations. I ran into that issue in 2004 with a woman who was born in 1907. I had to either prove her death, or wait until the 100 years from her birth had passed. I should have known better right away. I can get it now if I want to, but the drive... meh.

I really hope that by now your uncle has received his certificate; it's just rude to leave him hanging this long.