I don't have any real good suggestions - having been going through this myself for the last 6 months!!!!!!! At least now he has stopped the screaming for the most part
I find that I just do it really really really quickly!!!!!! So have everything prepared in advance, rip the old one off and put the new one on as quick as my fat little fingers can go.
I also have a stock of toys near the change table, so I can keep giving him other ones, in case its a pooey nappy and lots of time wiping is needed!!!! Oh, and I have a wind up toy that plays a tune, and its just small enough for him to hold by himself.
Other things I do is - first change in the morning - I do it at the same time as he is having his bottle, so he holds his bottle and drinks and I do the nappy change. I also do this at night before he goes to bed with his other bottle for the day. Usually there is one that my DH is home for to help so he distracts him with stupid games or singing whilst I change... but my GOD its hard somedays!!!!!! I hate changing nappies when I am on my own - its so frustrating. Another thing, because the bottle thing works so well, I also take his water sippy cup in with me so if all else fails I can try to get him to drink out of that, or have a book ready he can hold...
Not really good suggestions, but if anyone else has some that would be great for me too!!!