RS-485 is suitable for your application as it offers a two-wire communication mode in which the transmit and receive wires are tied togther (the Rx+ and Tx+ are wired to each other as are the Rx- and Tx- signals).
The FP-1000's can be used to convert RS-232 to RS-485 but do not support two wire mode so they are unsuitable for this scenario. You can get RS-232 to RS-485 converters that will support 2-wire mode. Two wire mode does not allow for simultanous transmission and reception, so a protocol/handshaking method must be programmed in your LabVIEW code such that only one FP-20XX module tries to transmit at any given time.
Regards,
Aaron
LabVIEW Champion, CLA, CPI