so I am starting a new PC. I got to Falkreath, mead in hand!

but the jarl won't be a dike and ask for the mead, which will then let me eventually be a thane.

how do I work around this?

I tried going to dengeir and doing stuff for him, no help.

Have you tried "Helping the people of Falkreath Hold." yet? It seems to me that I didn't get the option from him the first time I talked to him either. Does need to be done first?

That's strange. My PC's usually go to Falkreath first (when avoiding the main quest) and he always has the option - even at level 2. I don't think helping the people starts it.

Did you try the other dialogue options about how he became jarl? Or have you started the Civil War questline? I understand that can screw up becoming a thane in Falkreath Hold. Maybe you can do one of the other bounty quests (gotten either from the steward or the barkeep in the inn in town) to start it.

Good luck with it.

Do you already have a Get Person X Object Y quest active?

If you're already doing one of those quests for Ysolda, Captain Aldis, Lami, Torbjorn Shatter-Shield, Siddgeir or Rustleif, you won't be able to start the quests for anyone else until the one you're doing is complete.

I second this. The items the aforementioned NPCs may have you looking for could be (in order) a mammoth tusk, the book The Mirror, the book Song of the alchemists, and amulet of Arkay, or the book Night Falls on Sentinel. So if you have one of these quests up and running, it may be blocking the Jarl from giving you his for the mead.