"It's not a no, it's a not right now." This mindset has been game-changing for me in maintaining connections with others while declining invitations and requests. I let the person know I'm unable to commit, but ask them to keep me in the loop and consider me for future invites. This lets me show appreciation for being thought of and interest in what's being offered to me without having to overstretch myself. No further explanation needed. It's simple yet powerful.
The best route to take when declining or saying no to commitments that do not align with your goals is the direct route. Some people may argue that being direct is impolite but I disagree. Being direct saves time, both yours and the other party involved. There is no need to beat about the bush trying to come up with an excuse because everything you say will sound like an excuse. The best way to say no is to simply be honest. As a self-employed dancer/choreographer, I often work hours that do not coincide with those of my friends who work regular 9 to 5 or 8 hour shifts. I work contract jobs which often require that I put in hours during the weekends. Sometimes, I have to say no to invitations from friends because I understand that even though being self-employed means that I am in control of my own hours, I still have an obligation to meet deadlines and ensure that my clients are receiving the best service that I can provide them. I am clear and honest with my friends about my situation and try to reschedule hang outs whenever possible.
I simply let the person know that I am busy with other priorities. I feel it's important to be clear and direct so 1) they don't feel like they are being singled out and 2) they understand that I am careful with my time.