How to say not right now, and mean it.

Not right now doesn't mean as soon as the other person wants it - it means as soon as you are able to safely handle it within your boundaries, priorities, and other responsibilities.

Here's what that looks like.
"I will be able to do (x) after (a, b, and c) are completed."
"I am not able to (x) at this time. I am available at (x) time or (x) time, which works better for you?"

When you say not right now, you mean not right now, because you have conflicting priorities.

Don't drown yourself trying to help someone else not sink their own boat.