Hi,
Implementing any new feature and not making it tedious is an admirable, but tricky, goal.
Random events would spice things up a lot but if they were any more than minor impact ones it'd be shifting the game towards the RNG gods as, being random, it's hard for the player to develop a strategy to counter them. Maybe if you flagged the big ones ahead of time, eg. 'news of an apple blight on neighbouring islands', it'd give them a chance to prepare?
Another idea would be to play around with your 'new land' mechanic. At present new land tiles turn up for free at a regular interval. You could instead have a temple building, that once built, can be clicked on to trigger another set of 5 tiles, for example. This would be the only way that new land tiles arrive but everytime you pray to the Gods of the Little Lands the intensity of the pirate attack amps up a notch (frequency remains the same but pirate ships get more hit points).
This wouldn't affect your economic balance in any way but would give the player a trade-off decision of extra land vs. a gradually increasing pirate threat. It'd also tend to place a higher value on land and have players thinking more about what building to put where. If lands is scarce those become more interesting decisions and keeps the tension going as you are forced to expand while dealing with a Pirate threat that scales with your expansion.
But, hey, ideas are easy when it's not your game and it's somebody else who's going to have to implement it and make it work.
Best of luck.
Cheers,
Plugger.