I have an potential application that must cope with 2 stop bits and was
    considering doing the coding in one of the Basic codes. Is this possible?

Receive code written for one stop bit will work fine if it gets two stop
bits (the extra stop bit looks like a bit worth of inter-character gap.)

Transmit code that only generates one stop bit MIGHT have trouble being read
by two-stop-bit hosts if data is sent with no between-character gaps, or it
might not...

BillW