you can change type of the missions in the mission screen, as well as fraction and the level.
If you have preferred AI fraction - research main diplomacy technologies, bribe them, start trading -> cease fire -> send envoys immediately to all their planets, ask them to do the same, go for the easiest level of the mission.
When both of you have discent amount of envoys - 8-10 in total - it is a matter of time to reach scoring of 10 and above.
If it is 3 AI map - you can do the same with another AI of your choice - but chose wisely, because the remaining AI wont be willing to raise negative score with bribing for ceasefire. Perhaps you can try purely diplomacy orientated strategy right from the start, before getting penalised by other fractions for not completing their missions. So you could theoretically be able to build relations with all your AIs.
However, there is a drawback - I do not know how to make your opnonet to offer you pacts.
Is it a matter of supply and demand, so is you have good relations with a couple of AI, they just start to compete either you have to sit tight for them to research pact since those are not their priority...