Racial and diplomatic inclination are base statistics that determine starting standings with another player, the former is obviously based on race (different races have negative racial inclination.) The latter is based on factional relations, TEC Rebels have a horrendous base diplomatic inclination to just about everyone for example. I believe it can be boosted with the techs GoldenLegion mentioned. Diplomatic actions is based on, well, what you've done during the game, if you've given them money, sent them envoys, etc.
Anyway, I believe the problem is that your opinion of them wasn't going up, but their opinion of you was, right? If that's the case, give them missions, ask for money, ask for envoys, etc, your opinion of them goes up the same way their opinion of you does.