Few basic tricks:
- the 'send support' mission (forget the actual wording) can't be refused and gives you a small boost - repeat twice a year and it adds up. The only potential cost is that you are notionally committed to backing them in a war but you can opt out
- trade helps, simply buying their goods pays off over time
- your tariff rates have an impact, if they are low then people come to like you
- a good war can help ... if you don't use up the warscore at the end then that is added back to your diplomatic relations.
There are also events that will change your relations over time