Oh I can so relate to this!!!!! Since my little one could walk (just after 10months) she REFUSED to lie still for me to change her nappy. It always ended up at me screaming at her, her crying hysterically and me holding her down with one hand while putting on her nappy with the other hand.
SO..we ended up TWO people changing her nappy. Daddy does the whole 'keeping her busy part' and I do the nappy changing (as quick as possible). I don't change her clothes while she's lying down, I only do the nappy while she's lying. I close her door and let her run around in her room and when I can catch her I dress her

It sound like alot of hard work, but rather a happy baby running around and me crawling after her trying to get her arm into her shirt, than her and me both DREADING nappy changing time.
I also leave certain toys at the changing table which she ONLY gets when I change her nappy. Or I let her play with my cellphone (which she's never allowed to otherwise) for the 2minutes it takes me to change her nappy. We also play music/the radio while we change her nappy. It took about a month or 2 but now nappy changing isn't dreadful anymore and daddy isn't needed anymore to keep her busy:)
Sorry for the long post!!