This is such a fun pairing to explore because you get to play with two characters who express affection almost exclusively through aggression and competition. The tension writes itself. A really classic setup is the 'fake dating' trope, but make it for a Mugen Train mission. Imagine Douma needs to blend in at a festival to track a demon, and his cover is being there with Inosuke, who he's convinced to play his volatile partner. The comedy of Inosuke trying to act 'normal' while still threatening to fight every stall owner, contrasted with Douma's unsettlingly serene performance, is gold.
Another idea I've seen done well is a body-swap scenario post-final battle. The sheer chaos of Douma's calculating mind in Inosuke's impulsive body, and vice versa, could lead to some unexpectedly poignant moments. Inosuke, forced to experience Douma's emotional numbness, might gain a weird, grudging understanding, while Douma trapped in a body ruled by raw sensation could actually start to... feel things. It's a great vehicle for forced proximity and character study beyond just the usual enemies-to-lovers beat.
Honestly, the best plots for them lean hard into their contrasting energies—the cold, manipulative charmer versus the hot-headed, instinctual force of nature. Whether it's a reluctant alliance against a common threat or a strange, codependent resurrection plot, the dynamic is endlessly sparky.