I'm sorry I didn't see this thread earlier. Brian5470 is absolutely correct that you do NOT -- repeat -- YOU DO NOT NEED A SYRINGE TO FILL A JOYE 510 CARTOMIZER!!!
It's the simplest thing in the world. Even if you have brand new empty Joye 510 cartomizers, you don't need a syringe, you don't need to pop off the mouthpiece and dig out that little barrier piece. All you need to do is hold it with the threaded end up at a slight angle like when pouring a soda or beer. Place a drop of your liquid on that center hole in the threaded end and watch it get sucked inside. Repeat with another 15 drops or so, maybe up to 25 if the liquid is thinner and/or if the carto is brand new and empty.
If you see juice starting to dribble out of the mouthpiece, it may be full, or it may be that you have it positioned in such a way that the juice is flowing into the air shaft leading to the mouthpiece. There are a few ways to prevent this, or to minimize it, and thus get more juice into the filler material and less into the mouthpiece.
#1: This takes less than a minute, start to finish: every 4 drops or so, stop dripping and give the carto 4-5 sharp taps on the table or something hard, as if tamping a cigarette. This forces the juice down into the filler and breaks up any air bubbles interfering with the flow. Before doing the next 4 drops, rotate the carto about 1/4 turn. This helps to distribute the juice flow a little more evenly, and if you are hitting that spot that leads juice into the mouthpiece, at least you'll only hit that spot 1/4 of the time.
#2: This is a one-time step I do with each cartomizer, and it only takes a minute or two, but it helps a LOT in preventing juice from running into the mouthpiece. Before starting to fill as in version #1 above, go ahead and pop off that mouthpiece and dig out the little barrier inside. Take a simple regular size paper clip and straighten out the outside loop so you have what looks like an elongate letter P. Insert the straightened segment of the paper clip inside the mouth end of the carto and slide around the inside wall, probing for the air shaft. When you find it, the wire will slide down inside the carto, down to the atomizer area near the threaded end, but inside the carto. The loop part of the paper clip will hold it in place. Now take something with a sharp tip, like a small screwdriver or even the end of another paper clip, and make a mark like an X on the plastic tube of the carto right above the metal tip and in line with the paper clip loop above it. This little scratch mark will now show you where the air shaft is when you are filling the carto from the metal tip. So you can now hold the carto with that X at the top, so any liquid you drip into the metal tip will flow down, away from the air shaft. Again, this is a one-time deal to mark where the air shaft is so for all future fillings, you know how to avoid dripping into the air shaft. Now you can fill as with version #1, but you don't want to rotate the carto, just keep that X at the top while filling. Now you can just hold it at a slight angle, X at the top, and drip in 4 drops, then tap several times, then another 4 drops, then tap, then repeat until you've gotten about 16-24 drops inside, or until you see signs that it's full.