Only one serial line?
Not sure what you're talking about. In a previous project, I used a PIC16F628 with two pairs of serial lines as a sort of translator between 9600 and 2400 baud, and I had no problems at all. One pin for 9600 in, one for 9600 out, one for 2400 in, one for 2400 out.
Actually, now that I think about it, I used another one for 9600 out to a serial LCD for monitoring purposes as well.