Ring any Morgan dealer, or perhaps even more usefully, any other classic car workshop in your area - and ask them who they use for balancing splined wire wheels.
It cannot be done accurately with just the standard cones used by most tyre places, but you should find someone who can without too much trouble. Whatever you do, get them to use stick on weights not the dreadful hammer-on type (that the factory use, bless them!) that mar the rim surface, especially if painted or chromed, and then allow corrosion to start.
