In my 25+ years of boating I've actually never dropped a deuce on a boat before, knock on wood. The only time where I ever came close to being in an "emergency" situation was actually last summer. I was fishing for salmon and got one within about 30 minutes of being out, but the following couple hours after that were pretty slow. Then I have no idea what happened, if I turned or bent over in a weird way, but I went from not even thinking about needing to drop a deuce to being at like an 8 out of 10, with a 10 being imminent. I pulled up the gear, cruised back in, put the boat on the buoy, climbed over onto my kayak to sit in and paddle back into the cabin. When I climbed in, it hit me. Slowly and very methodically I paddled back into the beach, where it was unfortunately a low tide that I had to walk over to get back to the cabin. Halfway between the waterline and the cabin it hit again and thought I was going to have a "code brown" situation right in front of the entire beach. Luckily it was only about 8:30 or so in the morning and most people were still asleep or indoors and didn't have any idea as to what was going on. I made it back to my cabin in the nick of time and it was a near photo finish. As mentioned above, I always try to go before going out on the boat and then not eating much while I'm out there so that I can hopefully avoid any "issues" while fishing.
