As with most systems, you simply send it as two (or more) 8 bit bytes - however 3v) seemed to think it was already 15 bits.
Manchester coding though is a packet system, so lends itself to multiple byte packets.
EDIT:
I've just checked the datasheet (the device is long discontinued anyway), and it's 8 databits only, so you'd have to send ten bits in multiple bytes.
The obvious solution is not to try and use ancient crude remote control IC's, but generate and decode Manchester coding in your existing processors. If you can't do that?, then use ready made chips for it - like these: