Yikes ... you'll need a midi merge somehow. They made them in rack form and pedal form years ago, but I haven't seen one in ages.
You need to have Midi out(Tyros) feeding the TC in, and Midi out(Korg) also feeding the SAME Midi IN on the TC.

Here's one I found:
http://www.amazon.com/MIDI-Solutions-Merger-Input/dp/B0002GH8LQ

Make sure the keyboards both send midi info out on the same channel, and only let ONE style player at a time be used.