OK, I looked into the transfer button. To transfer people, it says the other country population can't go below 100M. Since my conquered 'slave state' has only 14M, I'll be waiting a very long time.
But you said 'transfer professionals'. I can't find that...
Also,
You can click on "direct trading" (on left), Click on "Population Transfers", and then click on "bid coins for population transfers". You can bid gold coins for 1M people. The problem being, the minimum bid is 6GC, and almost nobody ever wants to pay that much.