The standard PC UART clock input frequency is 1.8432MHz, which divided by 16 and then further divided by the baud rate divisors, will not provide the baud rate you desire. Some PCs have enhanced UARTs that can provide higher baud rates, and thus more baud rate flexibility, but I believe that you will still not be able to achieve anything close enough to 93,750bps to work.

I would recommend that you look at some of the expansion slot based serial boards available on the market. Some of these boards do not use the ubiquitous 16Cxxx UARTs and might offer more baud rate flexibility.