I did the conversion on a 99 Accord.
Go here: www.car-part.com
You want to buy COMPLETE rear uprights (hub assembly, disc, caliper, parking cable, and contol arms from a similar year Civic with stock rear discs.
You take the entire assembly and bolt it right into your Civic. Hook up the parking brake cable (it will fit right in). Hook up the brake line, and you are done.
You can try local yards but I would highlt recommend Car-Part.com Call up yards in the midwest where there is no salt induced rusting.
I did this and it was just that easy. The parts were very well priced and shipped to my door. Stuff was rust free and very clean.