How to further boost relations with subject: via war.
By rival province you mean a province from one of the gb rivals?
Yes. With one war, you should be able to combine three or even four bonuses, so long as GB's rivals and enemies overlap, as they often do.
You could get a total of another
+70, from one war:
- Check their Rivals and Enemies, and find a nation that is both a Rival and an Enemy, and whom you can DOW and beat fairly easily.
- DOW their Enemy, and you instantly get Declared War On Enemy, +10.
- Allow enemy troops to infiltrate the subject's territory. As soon as one of them is being sieged, go attack the enemy there, and you get Defender Our Territory, +10.
- If the siege completes, and the province falls to the enemy, that's even better. Go kill the enemy while it's in another of the subject's provinces, to get the Defended bonus. Then re-capture the sieged province, to get Liberated our Province, +25.
- At the end of the war, annex a province from any nation that is a Rival of your subject, to get Conquered Rival Province, +15.
- Finally, at the end of war you will get Fought To The End, +10.
Totalling
+70.
There is a further, juicy, bonus available if your subject nation has any cores owned by other nations, whom you can DOW and force to Return Core. This gives:
Returned Core To Me, +40 - per province! You can push relations to max +200 with this, in the right circumstance.
If you got very lucky and were able to DOW an enemy who was an Enemy, Rival, and who had cores of your subject, you could get
+110 for a single returned province, or any amount higher if there's more to Return. Of course that will be pretty rare. But it's worth noting that if your subject does have cores out there, it's probably worth just going for Returning those Cores and not bothering about an Enemy/Rival war; +40 is probably enough on its own. Then again, if the subject still has other cores out in the world you can Return, why would you want to integrate them yet?
That's a lot available! So prioritise what you need. One might want to not bother with Conquered Rival Province as that requires annexing and AE.
And Liberated Our Province, although it's the largest modifier at a juicy +25, might also be a lower priority because it requires letting the enemy win a siege against your PU-minor, which might be tricky and time consuming if the PU-minor and your other allies keep fighting him. Though you might get lucky and find the PU-minor attaches its armies to yours, and so you can decide whom to attack or not, and allow their provinces to fall so you can re-take them.
With +70 available without cores, or +110 available with Return Cores, it should be easy to get the +25 or +30 anyone might need in any given circumstance. Or get more to give yourself a buffer, so that it doesn't matter if Improve Relations drops a little below 200, or even if a Gift expires.
Note that for the Rival-specific bonus, Conquered Rival Province, it only requires that you go to war against a Rival; not that you actually DOW'd that Rival. So if you can't find a nation that is both an Enemy and Rival of your subject, but there's an Enemy who has an ally who is a Rival, then that works too, so long as you can annex one of their provinces in a resulting peace. Just make sure it's the Enemy you DOW, as the Declared War on Enemy only works for the nation you actually declare on.