1. Viking!Gellert (99% authorial kink) - Convicted of witchcraft, Albus has been chained up under a cliff and left for the tide when Gellert’s ship arrived and Gellert decides to take Albus home as a bed warmer (it gets cold in the Nordic). Frankly it would make more sense for British dark-age muggles to use ropes instead of rare metals if they were going leave Albus to drown because they were too lazy to gather firewood, but authorial kink demands that Albus be chained up like a maiden left for Cetus* and stuck shackled at the wrists till they get to a good Blacksmith so Gellert has to handfeed his new pet.
2. Roman!Gellert (because Albus is too English to be anything else but Gellert has the mystery place of origin and the Roman army was multi-racial anyways) - Emperor Grindelwald claims Prince Albus as a spoil of war / gift to seal a treaty. Albus would secretly or not so secretly like it because he was partly offered up because he wouldn’t marry a princess anyways. Pillow talk includes statecraft, trades standards, and alchemy. Squee at the sweetness of Gellert gifting Albus with a palm-size emerald so Albus wouldn’t have to squint to read small print.
3. Camelot-ish: Archmage!Albus has to convince the wayward royalbrat Gellert to take up the dreary responsibility of the throne. Somehow Gellert would seduce Albus from a tragically wasted life of celibracy as Albus keeps catching Gellert naked in public (PS Jamie Campbell Bower frolics nude in the Camelot series on Hulu and CBC)
4. Paper Kingdoms (aka game-of-thrones-ish AU): Albus and Ariana were on the run after the murder of a local lord that had branded the Dumbledores traitors to the hallowed throne, and they were suspected of letting in the raiders. Then they fell into the clutches of the newly crowned just-as-mad King Gellert, who is suspected to have murdered his late cousin., and has the reputation of being a sadist. Albus goes to Gellert’s bed in exchange for the promise that his sister would be left alone, and sometimes has to beg for the privilege and plead himself to Gellert as the better plaything. Really though, Gellert only has eyes for Albus from the beginning, and only expressed interest in Ariana knowing that Albus would offer himself up (especially when Gellert heavily hints at it).
5. Triwizard AU (canon time period with a nail divergence) The tournament was never discontinued in 1792 – or it resumed in 1898 - just in time for Gellert Grindelwald to meet Albus Dumbledore. Star student Albus goes to the tournament in Durmstrang! Meanwhile it turns out the tournament only resumed because of a dark wizard/witch’s ploy to use the strong magic of the victor as a sacrifice.
*Cetus: in the school library version I read, Andromeda was to be eaten by Cetus the sea monster, but wiki cites a version where Andromeda was chained naked to a rock for Cetus the sea monster to /ravish/. Because this myth is Greek instead of Japanese though, Cetus is described s whale or shark-like instead of having tentacles. So have a fun brainmelt picturing Hoshigaki Kisame pawing at Toby Regbo or Lily Collins.