You can get some diamonds occasionally from quests. In earlier ages I think u can get perhaps about 100 or so diamonds per age from quests. In later ones there seem to be more often them, about 150-200 per age is not unrealistic estimate. It can add up to about 1-1.5k diamonds if you complete the whole game and do your quests. This number can also increase a lot in PE/ME if you build Chateau GB. Also there is a bonus EMA province which awards 100, bonus LMA province that awards another 100, bonus InA province that awards 150 and bonus ME province that awards 200 diamonds. That is further 550 diamonds. Wishing well was already mentioned, you can earn 50 diamonds roughly every 3-4 months from 1 well. Also there are special events during more major holidays etc which often reward diamonds or include a chance to win diamonds. During the summer event about 5 months ago, it was for example not rare for people to win more than 1k diamonds per world.
Now know that diamonds are all the same from all 8 worlds. So if you win diamonds on Arvahall, you can also use them in Brisgard. I for example have advanced towns on all 8 worlds to ME or on verge of it, but have chosen to spend any diamonds won only in my original biggest world. I have not counted, but I'm pretty sure I've won more than 20k diamonds total by now. But remember it has taken me more than 1.5 years and I have participated in all of the best events etc.