I refused to basically run a 40 patient geriatrics unit alone when I had zero experience. I confronted my superior, told him that I felt incompetent for the job and he ended up consulting me every day, like he should have in the first place. That was an easy call, I was scared shitless.
I've never had a problem with saying no and don't understand at all why other people do. I consider myself much less compassionate/symphathetic than average, i.e. don't feel other peoples emotions. My empathy is pretty intact though.
Just begin with sorry...
If those don't work, I come up with a white lie. If they keep pushing it, I have no problem with being blunt.
Some people seem to be a bit too generous for their own good. I know a precious few people who are especially good at saying "no" when asked to take on new responsibilities that would put them over their limits. I love working with people like that because I can always trust them to tell me when it would be better for me to find someone else to do the thing. I expect this to be an extremely valuable skill it would probably be good for many of us to understand, learn, and be able to teach to people who really need it.