Why do you need a syringe to refill? Carts don't need a syringe. Standard stuffing cartomizers don't need a syringe though some like to use one down between the inner metal wall and the stuffing. Reservoir cartos specify a particular kind of syringe - some want a sharp of a particular gauge and some want a special flexible tip on a syringe.
If you have tiny carts that push over an atomizer, you don't need a syringe. You can push the little
juice cup up by sticking an unbent small paperclip in the mouth hole.
Many juice vendors, many multibrand ecig hardware vendors, and every DIY vendor sells some kind of syringe. LiteCigUSA.net has one, OneStopDIYShop and DIYFlavorShack have them