Hi Lauren
we've had this bigtime with our 10mth DD for a while now and here's what we've found works, or at least makes it less traumatic - giving her plenty of things to fiddle about with (like a large basket with spare vests and sleepsuits etc), letting her stand up to pull her musical rabbit mobile (and getting that nappy off/wiped/clean one on double quick whilst she's doing it), learning to put the nappy on her whilst sitting down - basically anything that distracts her and means that you're not making her lie on her back, so I often finish off tricky things like tights or trousers by sitting her on my knee afterwards. I also 'fly' her onto the change table to make her laugh before starting so she's not tense or anticipating a tussle.
We really find that working round her imperative need to be mobile and not on her back, took the traumatic fight out of things and helped us to feel less frustrated by it - yes, its much slower these days but she also is cooperating more by things like helping to put her arms into her sleeves etc and we praise her up loads for it.
Hope this helps and I guess it's good practice for some of those toddler territory issues to come....
mama davies