If your engine won't stay running at idle, you need to look at a few things.
First of all, does it slowly drop rpm's until it dies, or does it just die as soon as you go to idle? If it slowly drops off rpm's and then dies, I would be looking at cylinder balance. Maybe one cylinder is weak for whatever reason. I would check compression on all cylinders and see what you have.
If it just dies at idle right away, I would guess that the carb needs to be taken apart and cleaned. It sounds like the idle circuit is blocked. If you can tell me what engine it is, how many cylinders, how many carbs, etc., I'll try to help.
Does it run on all cylinders as it is dying or does it drop one out?
I have found that the majority of run problems on boat engines is fuel related. These things sit for extended periods without running. That causes sediment and condensation problems in the fuel system. I can't tell you how many carbs I have pulled off that have garbage laying in the bowls. Get all that stuff cleaned out, blast throught the passages with some carb cleaner and put it together with new gaskets. Believe it or not, they will run pretty well even when they are neglected. It takes quite a bit to actually kill one.
My Mercury 35hp that came on my Sea Nymph wouldn't run at idle when I first got it. It would rev up fine and run at speed, but as soon as I came down off the throttle, it would die. After I pulled the carbs and cleaned out the bowls, ( it had two carbs), it ran great. Simple as that. I also had to adjust the linkage a bit as the advance linkage was way out of whack from the previous owner playing with it. He had the advance way retarded and it hurt the top end. I got the manual and found out where it needed to be set. After doing that, the engine ran pretty good. The bowls had a bunch of crud in them and it would float around in the fuel and block the idle jet. Once that was cleaned, it ran fine.
Be certain that your fuel line is good and you have no air leaks, although that would normally cause poor top end performance as the engine gets starved of fuel. However, as many small outboards use a vacuum pulse to work the fuel pump, a weak running engine won't give you that strong vacuum pulse to work the pump and the engine runs out of fuel.
Sometimes you can clear a mildy clogged carb by warming up the engine, revving it up in neutral IN THE WATER, and clapping your hand over the intake. Sometimes that will suck a piece of dirt through the jet that it is clogging. The motor may cough and sputter, but if it works, it will suddenly begin to idle properly, at least until it sucks up another piece of dirt. Give that a try and see what happens.
If you need more help, you know where to find me.
UFM82