This may seem counter-intuitive if you've played Tropico 3 or 4, but try setting the budget of all workplaces to max from the very start of the game, and keep it up throughout the entire game (shift-click when setting the budget so that any time you build another of the same building type going forward they'll also be set at max). While overall happiness does seem to be a factor, it seems that job satisfaction plays the biggest role in immigration. Setting the budgets to max does increase expenses somewhat, but all of your buildings will also have a +25 effectiveness boost, which I've found more than offsets the expenses, even if you have several buildings that don't generate revenue such as teamsters, construction, etc (they don't generate revenue, but they perform better/faster). In addition to the increased job satisfaction, your entertainment and religion buildings will be much more effective, which further increases happiness.

I've found that doing this allows me to pretty much fill any vacant jobs within 1-2 ships docking. I try to keep the open jobs to less than 20 (not being fully-staffed reduces building effectiveness, so you don't want to expand too quickly--just pace yourself), but again, they fill very quickly. While I can't say for sure since the documentation for this game is non-existent, it definitely seems to me that even if you have high-happiness and job satisfaction, immigration will slow down when you don't have open jobs available, so unemployment does not really become an issue until late in the game (which is going to happen regardless). Again, if you've played previous versions of Tropico this may seem wrong, but just give it a try. I was skeptical at first, but I've found that doing this has made my economies get off the ground much faster and stay stronger through the entire game. My end-game cash totals are at least double what they ever were when keeping the budgets at 3, and your happiness will rise quickly and stay high through the game.