How do I purchase tickets for the Night Riviera sleeping compartment?

According to https://www.seat61.com/Cornwall-sleeper.htm the bookings can be bought at https://www.gwr.com and for pick-up at the station when you travel.

The Man In Seat 61 says that GWR doesn't accept foreign cards, but I had no problem buying an Advance ticket through their website with a Danish Visa card earlier this month. That may be because the card was at least European, or seat61's info may be out of date. They did require "Verified By Visa" authorization.

Unfortunately The Man In Seat 61 also says:

You cannot book berth supplements to go with existing tickets or BritRail passes other than in person at stations.

and indeed I can't get www.gwr.com to make a booking for just the cabin supplement when I try. Similar experience on thetrainline.com. You could try calling GWR directly at +44 345 7000 125 and hope this is also outdated information, but I wouldn't be optimistic.

If you already have a train ticket and just want a berth supplement, you will need to telephone GWR I'm afraid. As far as I am aware, there is no other way of purchasing these from abroad for the Night Riviera (the Caledonian Sleeper website now sells them but only for the Scottish sleepers; not the Cornish one).

Telephone them on +44 345 7000 125, and tell them you already have a ticket and want to purchase a berth supplement. I believe you should be able to do this over the phone, at least if you manage to get through to the right people.

If this doesn't work for you, your only other option is to try to buy one at a station as early as possible when you arrive in the country. If you think you're not travelling at a busy period this may be feasible; otherwise the train might be sold out. In any case, it's risky for this reason. I also find that some ticket offices are better than others at knowing how to sell these!