Any 10ml syringe will work, though you would have to use it 3 times. Depending on the type of liq you are using,a larger needle does better with higher concentrations of VG which can get pretty thick. But, as most have mentioned, the needle portion most often just screws off.
If you are looking for a larger capacity needle, many DIY e-cig vendors carry them (along with pipettes) or you can go to your local Tractor Supply store and purchase larger needles used for farm animal injections.