The first step, surely, is to get a tether from a decent orbital height down to the apex of SpaceShipTwo’s flight level.
With a counter balance thats pulled in ahead of time slowly (using solar panels), SS2 could then be winched up using nothing but the stored gravitational potential of the counter weight.

While you have the hard part of “catching” SS2 at apex, its infinitely easier then having a full space elevator from geosycn to ground. (which mostly has to carry its own weight…even with carbon fiber your talking about insanely thick cableing).

This on the other hand, seems achievable with todays tech.