I think the issue you are facing is an important life lesson I had to learn (just an opinion). I think the real root of this issue is you feel bad. You don't like the idea of letting the other person down, and it makes you feel obligated. Maybe what I am stating is obvious, because if you weren't interested, and you felt comfortable saying no, then you would have by now.
The first thing I learned, is that when I pretend I am interested in something that somebody else is doing, they expect I truly am. I get their hopes up. They are starting to plan with me included in those plans. In other words, it's a waste of their time, and the sooner you say no, the better is is for them. So don't feel bad. You are helping them out and are helping them find somebody who actually is interested and will contribute sooner. And if you are friends with this person, you risk making the friendship/professional relationship go sour if you don't contribute like they expect you to. They might see you has phony or lazy which isn't true.
The second thing, is your time is important and it always will end up looking worse for you the more you try to cover things up. The more you lie or potentially act interested, the more he is going to push for ways to either keep you interested or communicate with people to keep you involved. He needs to know it's a firm no coming from you. You can say something like:
"Hey I really thought I had time to take on this project, but I don't. I have other things stressing me out that I need to take care of, and I apologize if I wasted any of your time".
Be firm. Don't act like you are thinking about it. If he asks what the problems are, just say it's personal. It's your life and he needs to respect that. You can also just straight up say:
"I thought I was interested, but I'm not I'm so sorry. I have a lot of other things going on and I would just be wasting your time".
Don't like either? That's fine, but realize if you try to say "my supervisor said it was a bad idea" he might reach out to your supervisor or ask you to reach out, then what do you say? Then it becomes obvious it's really you that just flat out does not want to work on it anyways and ends up looking worse for you. I would try to be as direct and honest as possible.