After setting up the DB on couch.io, I managed to access it via CURL, but it took me a long time and a hint by Alexander Lang to figure out how to tell couch_potato to use BASIC AUTHENTICATION. Actually, you cannot use the default CouchPotato.database method. You have to create your own database instance with the underlying CouchRest:
# define the CouchDB server through CouchRest
CouchServer = CouchRest::Server.new "http://user:firstname.lastname@example.org"
# create the CouchRest database
CouchRestDB = CouchRest::Database.new CouchServer, "database"
# use that with CouchPotato
CouchDB = CouchPotato::Database.new(CouchRestDB)
P.S. this also ended up on the GitHub wiki page of couch_potato.