A couple quick things to get out of the way
Just like every "what is the appropriate age" question, there isn't one. Age is a pretty decent approximation of the physical and emotional maturity of people, but its margin of error is very high. While some things have laws that put lower bounds on them (drinking, violent movies, staying home alone) the truth is that many people below that threshold are ready, and many people above the threshold are not.
So the notion of what age do you need to be to watch Disney films is a very misguided premise. Instead, we should be focusing on the physical and emotional attributes of the child to make the determination of if they're ready. Age is just one of these attributes, and isn't nearly as important as it might seem. I would also like to say that as the child's godparent, it's possible you don't have enough exposure to the child to really make the determination, and regardless of what criteria we come up with here, it remains the parent's decision. That's not to say you shouldn't care, because you totally should and clearly do - just remember to be patient and kind if the parents disagree and/or you're overruled. After all, being a good role model for disagreeing respectfully (a form of conflict resolution) is one of the best things you can teach a child!!
Okay, with those more abstract topics out of the way, let's talk about movies. The first criteria I would mention is attention span - is the child able to watch it for an entire hour and a half? My first child couldn't. Not with the distraction of toys, the outdoors, her sister, etc. It took her until she was about 3 before she could actually watch an entire movie. Once she was able to watch a movie in a room with distractions, we took her to see a movie in the theaters. She had been watching movies before, but only if she were being cuddled the whole time. But, that doesn't mean we didn't have movies - it just means she wandered around not always paying attention to the movies we had on. My second, however, was able to sit through a movie much earlier, probably around 18 months. I don't think it's so much that she has a higher emotional maturity than my eldest, just that she seems to enjoy them more and is less distracted by things.
The next criteria is comprehension - is the child able to actually know what's going on? If the child can't at least parrot/mimic some of the things they see in the show, it's probably not sinking in. At 1, I would not expect them to be able to do this, but that doesn't mean it can't happen. However, my children have been watching TV since long, long before they hit their first birthday. We've gone through enough Baby Einstein DVDs that we should have invested in their company! We also had a few DVDs of nursery rhymes which have a number of useful benefits (and just maybe we're prepping our children to play music with us some day and exposure to basic chord patterns at an early age is part of a grand master plan. Maybe.)
Okay, so far we have.. are they able to physically watch it for that long? And if they are, are they reasonably expected to gain anything from it? And I would say this applies to any film, not just Disney films. A big hit in my family is nature shows, and I would say the same criteria applies there.
Specifically with regard to Disney films, if we are to truly love our children we must be willing to filter the content they see. Whether it's film, books, friends, we have a duty to protect them. One of my wife's favorite movies as a kid was Cinderella, and as wonderful of a movie as that is, there are some concerns with it that my daughters just aren't ready to handle but they certainly need to someday. Should Cinderella's measure of happiness be that she gets married to a prince? Is it expected that someone who remarries is going to hate her step-children? Why are the mice saying "leave the sewing to the women"?
These are not simple questions, and they do not have simple answers. My two year old doesn't even have the necessary vocabulary to try to tackle these questions. My four year old probably does, but doesn't have a broad enough life context for it to make any sense. And she's at such an impressionable age any conversation we did have with her is likely to simply impress upon her my wife's and my views as opposed to her reaching her own conclusions, which is something we can't avoid entirely but would like to at least try to not make her a cookie-cutter version of us.
To make a long story short, you need to make sure you know why the child is watching the movie. It's really not much different than introducing anything else to a child through the years, whether it's brussel sprouts, swimming lessons, stand-up comedy, or beer. Once you've identified your objectives (which could be as simple as getting him acclimated to movies!) find an appropriate movie and try it. When you're done, see if you met your objectives.