You can improve relations by picking up effects that improve relations over time.

Having nests in your territory does this, albeit very slowly. The Neural Manipulator Wonder gives a much bigger bonus every turn. And I think one of the Harmony Affinity Quests also gives a bonus, but I don't quite remember.

It would be a bit nicer tho if there was a basis cooldown for aliens to "forget" your previous sins, just like the vanilla/RT version has. Having quests to get rid of aliens here and there, the leeches and sometimes too nosey aliens that block your ressources require you to kill them - with the result that you are doomed forever and even after 100 turns later they are blood-red mad at you.

That still exists in Codex. There is a slow, but constant trend towards the neutral point (being Orange in this Mod). Killing a few Aliens here and there should not have too much of an impact on your long term relations with the Aliens, but clearing Nests comes with a heavy penalty.

When possible, try to attack the Aliens with ranged attacks while not standing next to them, since this doesn't have any impact on relations.