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There are three options (as usual):
1. get a 51 with second hardware Uart e.g. 80C517 (old but many peripherals)
2. use the bus-interface to connect an external Uart e.g. 16550, the external bus-interface is a big advance of the 51 compared to PICs or the small AVRs.
3. programm a software Uart at your 51. Uses some processor-time and a timer but maybe fit in your application.
Application note from Philips (AN423) is ready-to-go software driven serial communication routine for 83C752/1 (These derivatives do not have UART...).
But there is a"BUT" in this approach: sometimes you will have problems with synchronization (at higher baud rates), specially if bytes are sent one after another, so my advice is to work below 9600bps...