kicker sputtering at trolling speed

I have a 2000 mercury 9.9 4 stroke as a kicker. When trolling at slow speeds 1.5 to 2.5mph it will slow down and speed back up to speed at a consistent rhythm. When it slows down it gets to the point of almost stopping but will kick back up to speed and slow right back down.It does eventually die. It also will not stay running in neutral unless I have it on high idle. At high idle it runs great. Its like its not getting a consistent flow of fuel at low idle. I was thinking maybe fuel filter, fuel pump? Any suggestions appreciated   

If it's a consistent cadence I might guess a sticky float.

Either way, I agree with the others who chimed in, time to rebuild the carb.

The low speed jet is plugged...

Soak the carb overnight in cleaner and she'll be as good as new. 

Pull the carb off and take apart and clean, low speed needle probably has crud, easy fix, get a can of carb spray cleaner. 4 stroke carbs are easy to clean.

It a 2000 mercury 9.9  time to get the carb rebuilt and tune in