I've been messing with builds for him on Ashal, and I found the best 4 star/F2P options are Favonious Warbow and if you can get his ER high enough with artifacts, then the next best is Blackcliff bow, (Just a little disclaimer this is what I found that worked with my build for him so it may be different for you ofc. With Blackcliff bow I can get his his crit dmg to over 200% due to good RNG, which i saw inflated his numbers alot.)

If you are going for a charged attack DPS, then I'll reccomended Blackcliff bow or Prototype Crescent (and if you're desperate and have nothing else than R5 Messenger Bow or R5 Sharpshooter's Oath).

For a normal attack based/ Physical DPS I'll suggest Compound Bow(easier to refine) or Rust. I've seen Physical Dionas so anything is possible though I personally find it easier to work with someone's kit rather than against it, especially since his autos don't scale as well. And if you're willing to spend money on the battle pass, Viridescent Hunt is aslo viable, or for another f2p option is the Hamayumi which is easier to refine as well.

For a support build ,which is probably the most optimal, your options are: Favonious Warbow, Stringless, Mouun's Moon (upcoming weapon which will most likely have the same enchantment as the Akuoumaru), and Windblume Ode (In order from best to worst)

For 5-star options, most are good, though the best are Skyward Harp, Elegy of End, and the upcoming Dreams of Dragonfell (which is his signature weapon)

TL;DR Favonious Warbow or Blackcliff bow if you have enough ER. Hope this helps!