Boyer Bransden ignition systems are normally intended to work with the original coil (or coils) setup, unless they say otherwise (as with some of their twin/triple cylinder kits).
So as it's probably a 12 Volt (the Triumph/BSA '64-on?) BB kit then you are likely to need a 12 V coil, although I don't know which Japanese type you would need but probably one from a points ignition rather than an electronic ignition model as the coil resistance is important for the BB system to work properly I think?
If you phone Boyer Bransden Electronics 01622 730939 (if you are in the UK), +44 1622 730939 (if you are outside the UK) between 9AM - 5PM (UK time) they are normally very helpful.