It is easy. The 19200 baud means 52uS per bit.

Unfortunately, it's also quite easy to do it wrong.

SoftTX = 1;             // start bit
delay_us(52);
for (i = 8; i--; c >>= 1) {
    SoftTX = c & 1;     // low bit first
    delay_us(52);
}
SoftTX = 0;             // stop bit
delay_us(52);

1. That would work only if the instructions between the calls to the delay routine are executed by the MCU in a negligible amount of time. Since the for-loop does quite a bit of work, and the MCU in question is a 12-clocker, this is questionable.

2. C does not give you any guarantees as far as timing goes. Write the whole thing in assembly.