Well, it's probably not available in the accessory barrel program yet, but it definitely will sooner or later, I would hope. It's listed in RSR Groups's wholesale catalog.
HRSB2-F20 H&R ULTRA VARM 204RUG 24" FL HB BL
Product Specifications
Manufacturer H&R 1871
Model Ultra Varmint
Action Single Shot
Caliber 204RUG
Barrel Length 24"
Finish/Color Blue
Grips/Stock Synthetic
Accessories w/Scp Mnt Rail
Type of Barrel Heavy Barrel Fluted
http://www.rsrgroup.com/cgi-bin/cgirpcux/WTM-002OAs far as your frame being used with the .204 barrel, only late built frames qualify, those calibers listed with asterisks are those that are critical, but the .204 isn't listed yet cuz they still haven't updated the page. What's the frame number on the BC? It could be only one year old to you, but still older built. The hornet "L" was built in 1997, the cutoff for the high pressure rounds is '98 or '99, IIRC. Not sure of this, but IIRC the BC frame is color case hardened just like the pardner shotgun frame, it could be an SB1 frame, for all I know... :?
http://hr1871.com/barrelAcc/index.htm