I agree with the prior answer that a rope should not be your permanent solution here, given that it will ultimately damage the tree. However, I think you can mitigate this for short-term use of rope, until the tree has stabilized itself and no longer needs human help, in one of two ways, possibly both:
- Chafing gear. Use scraps of other material as a pad between the
rope and tree. A tarp or other strong fabrics might work, but I think the best thing
here is to run the rope though sections of old garden hose before
tying your knots.
- Frequent re-adjusting. Every couple weeks, remove your rig and
re-do it in a slightly different place, allowing any friction damage that has occurred to heal. (It sounds like you already plan to do this.)
Given that, I think the rig you want is some form of trucker's hitch, which is not really a single knot but a combination of multiple knots. Working together, the different knots form a virtual ratchet strap that holds itself under tension.
For a couple how-to's, here's some links: https://www.animatedknots.com/truckers/index.php and https://www.wikihow.com/Tie-a-Trucker%27s-Hitch. Normally Animated Knots is quite good, but in this case I think they didn't do well in showing the distinct parts. Wikihow's drawings can be hard to interpret, but give a decent idea of what is going on.