i know that it is possible to pay tavern keepers, either with trade items or coin (if you have a coin type they will accept), because i spent some time figuring out how once, and i generally pay for my tavern purchases rather than just skip town. but it's been a couple of months since i've played much, and i can't remember the specifics offhand. but maybe just knowing that it's possible helps? (i.e. now you know to keep trying things, because something will work eventually)
i also know that it's possible to buy drinks in very crowded taverns and eventually get served, because i do that all the time too. i generally tell stories while i wait for my drink to arrive, cause it seems to pass game-time a lot faster than just pressing '.' (and if you provide entertainment, tavern keepers give you discounts)
npcs accepting currency is a crapshoot. if you can "ask or offer currency" and the maximum amount is nonzero, congratulations, you have a mutually acceptable currency. now you just need to guess how much stuff is worth... (or, install dfhack, and view the item description to see its value)
much of the time, merchants will have an inventory loaded with coins that they don't recognise the value of. in this case, you will see them in their trade inventory, and they will trade you them as objects for like $1 each (regardless of their face value). if you don't mind being an asshole, this can be a useful way to get a lot of money cheaply that maybe some _other_ merchant will recognise the value of
i haven't done any real science, or even checked mantis, but i think the "merchant has coins they don't recognise" occurs when there's some inconsistency between the npc's civilisation and the civilisation that controls the location the shop is in. i believe the npc only recognises coins from their own civilisation, but the "merchant inventory" handling stocks them up with coins from the local civilisation -- or something like this -- and therefore if there's been wars/invasions/coups/migrations/etc then it'll be a mess. i think this is probably less of a problem in worlds with a very short history, and more of a problem in worlds with a very long history