No I have coring bits but if you need to core a long piece of wood putting in my tail stock only allows you to go in an inch or two at a time so is there a different way
It depends on which lathe you have. The one with the leadscrew isn't strong enough motor wise to core balsa wood without a different motor.
If you have the one with the fixed head and the rack and pinion here's what I do. I get the gun drill started straight with the tailstock and then lay a scrap of wood 3 inches or so long on the dovetail at the back end of the tailstock. Then I bring the carriage up behind it with the drive motor installed on the lowest speed and slightly loosen the tailstock on the dovetail. The motor on the carriage feeds the gun drill right on through while you stand back and supervise. A nice dust collection device makes it clean and painless. Make sure your wood has at least a slight taper on it and drill the wood in the direction of pushing it tighter in the chucks or it can and will vibrate loose.
If you have the lathe with the leadscrew and have a stronger motor no doubt you could core in much the same manner.
JC