SPI is serial, so its not suitable to send it in through that. The only solution i can think of is to use the ports, e.g P0 or P1. The idea is that you have to synchronise the data coming in so maybe creating some sort of clock signal in the part, sending it out through a port pin, then send the data serially to the port and get the uC to capture the data there. the data can then be moved into the internal registers and played with. All you have to do in the 812 to be able to use the port pins (as far as i know) as inputs is to change the port configurations.

The question about TI and RI is confusing me, do you wish to use them to transmit data to the computer as they are part of the UART. The SFR you need to use with these is the SCON register, not SICON (i think, i'm working from the ADuC812S here). If you want to use the uart for anything else but the computer, you'll probably have to disconnect it from the computer after downloading and reconnect it. From the sounds of it, you cant do this so i would recomment the SPI interface for the serial data. A full explanation on how to use this is on the ADuC812 app notes, on the website if you already dont have it