You can use a 555 to act as a driver, it will drive the coil direct ( though you will have a lot of harmonics) and will drive at quite high current, plus it will act as a buffer for the drive quite well.
Just keep the matching network, and add local decoupling to the 555 right by the supply pins ( 1000uF 25V electrolytic) and the output will be usable for you. The drive only needs to be a square wave with 50% duty cycle, the filter and the LC of the coil will make it a sine wave for you, no need for any sine wave drive, the harmonics will not have too much effect, just like on the original one, which probably uses a square wave drive.