How do I bring Cockram and Burgess closer together?

The key to this mission is patience. As long as you are not detected, after you have found your targets (actually see them), they will start to take a predetermined route around the town. They will be walking around together so they should be easy targets to air assassinate when in range. You should not get detected during this part of the mission otherwise you'll get everyone riled up and your two targets will stop taking that route and split up.

You should (silently) take out guards that are covering the roofs or are within visual range of them. That way you can easily get into position to the nearest roof when they come by. Then lie in wait for them to get close enough and air assassinate them.

If you're having difficulty taking out enemies silently, take advantage of your sleep darts (and not your berserk darts) so you can close in and finish your targets easily. You don't necessarily have to take them out one at a time. If you spot a group, shoot them all with darts and finish them off.

I recorded a quick video demonstrating how easily this can be done:

Gunpowder method. I was having similar trouble with this today. However I might have found another method. While stalking the two targets I was spotted and all hell broke loose. I tried to hide but to no avail, they were on me like glue. I spotted the gunpowder barrels near where a large group of soldiers parade. Standing next to the barrels I took aim and waited till the two lads got close and blew us all up. This also counted as a double assassination. Provided you're not very low on health this could be a last resort if you get seen like I did.

It's probably a little late for this, but I just got into the game and was having trouble with this too.

After screwing up many, many times, I eventually got aboard the ship while they were on the docks. I play very slow and cautiously, so this happens every time for me. I carefully climbed the rigging and... screwed up, and they came onto the ship and fought me.

So what I did was drop a smoke bomb, kill some scrubs, smoke bomb, kill scrubs, and repeat until only the two targets were left. I hit one with a sleep dart, brought the other guy near him, and hit that one with a sleep dart. A short climb half way up the rigging and they were both available for a double air assassination. Easy. Stupid, counterintuitive, and I daresay badly designed for such an objective, but easy.

If you don't mind exploiting AI and implying that in a true historical event Edward Kenway lured two men onto a ship, put them asleep, and then dove at them like some damn lunatic from a story and a half up, go for it. It bugs the living hell out of me to do it this way, but it's done.