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Honestly, at this point, they can't do him justice. He story is entwined with Thor and Asgard's so much that if the MCU tried to adapt Beta Ray Bill, he'd end up a different character.
In the three origin stories for him I've seen (comic, Earth's Mightiest Heroes, and The Super Hero Squad Show) he enters the story by kicking Thor's ass, before doing the impossible and being the first person (other than Thor) to lift Mjolnir. He then goes on to earn himself a new hammer (given by Odin in both the comic and Earth's Mightiest Heroes versions, and by Mjolnir is Super Hero Squad) named Stormbreaker, and become Thor's sworn brother.
Bill is also thoroughly connected to Marvel's version of Ragnarök. Surtur destroyed Korbin, Bill's homeworld, (except in The Super Hero Squad Show continuity) and Thor meets Bill on a ship full of Korbinite refugees who are in stasis. Later on, Bill fights alongside the Asgardians during Ragnarök, before Thor teleports him away, as he doesn't wish to see Bill die and believes Bill should be with his people.
In the current comics, Stormbreaker has been destroyed and Bill wields Surtur's sword, Twilight. However even if the MCU gave Bill this weapon, I don't think it will work, as most of Bill's character development and story, happed with or alongside Thor's. I wish we could have gotten the "Ballad of Beta Ray Bill" storyline in Thor: Ragnarök instead of the "Planet Hulk" lite stuff we did get.