The Tynwald has a similar problem to the Althing, though. In that at some points in its history it didn’t wield any actual legislative power over its little island, despite actually meeting continuously.
San Marino looks like it could be a good bet. Prior to the late mid-1200s it appears it was (despite its status as an official Republic) ran by a council of powerful families–the Arengo (thus an oligarchy, not a democracy.) However since 1243 the “Grand and General Council” which was elected by the people appears to have run the country.
However San Marino suffers from the theory versus practice debate. During the early 20th century powerful land owners made the Grand and General Council more and more oligarchical, and this culminated in the San Marino Fascist Party running the country for twenty years, so it becomes questionable if it was a true democratic state during that time.
I would not immediately discount a state just because of franchise issues, I think you can have a functioning democracy without a totally inclusive franchise. To me it’s about decision making, where is the primary decision making power, in the hands of unelected powers or in the hands of powers beholden to the people? At some point if the franchise is super small, like 1% of the population, or just a small cabal of potentates, that is an oligarchy and at that point the franchise issue would disqualify the country from being a democracy.
However I think that as long as the primary decision making power of a country is beholden to the people, even if just say, 25% of them, that’s enough of a benchmark to call that country a democracy.