To know whom to ally/give tributes . First do Research policy the diplomacy increase with. Then restart again.
Ally - if you have allied or they like you.
Neutral - most nations affected
Enemy - your enemies can be came neutral. Sometimes you need to have war with a nation to increase diplomacy which is weird
Diplomacy speed +1 can do wonder. Sometimes nation increase diplomacy without the above research.
Also having high administration points is better than economics lvl 1 in taxes.
Change gems (hectic but helpful) depends on case. Recommended skills
Negotiation expert lvl 2 or 1
Goodwill ambassador lvl 2 or 1
Interior management lvl 1
Strategist - must have due to spam units
Regarding to increasing border, some nations decrease diplomacy as you get bigger/larger. Ex: England expedition
Also if you can give tributes to nations so they will not start attacking you when you barely win with another.