Since the original poster bought a 5.56mm suppressor, and not a 7.62mm one, I'd go out on a limb and say that anything .308 diameter (Whisper/Blackout) isn't in his near future. Perhaps if he wants to spend another wad of cash and 6 more months waiting on a stamp for a new can that is a good way to go.
Loading his own is also a better option, allowing him to tailor loads to the varmints he is going after, and depending on whether he has a 1/7 rather than the more common 1/9 twist Bushmaster he may be able to go as high as 85gr Barnes Match Burners and still have a subsonic load which can be loaded to magazine length and may prove stable enough in his testing to avoid a costly baffle strike and still provide more than twice the energy of a subsonic .22lr for the odd coyote, provided his state allows suppressors for hunting.
As to shooting .223 factory subsonics, I will assume that he does not desire to buy another can, upper, conversion unit or reloading equipment and components. I will also assume that his Bushmaster is likely a 1/9 twist, and that he knows that subsonics will be turning his auto-loading rifle into a straight pull bolt action... and that he is totally fine with all of this and still wants some factory subsonics, like he asked about.
Engel Ballistic Research, Inc. makes what it calls 5.56mm NATO/.223 Ultra Stealth Match Subsonic. It is 63 grains, so it is likely to stabilize fine in a 1/9 twist barrel and not destroy his can. Doing a search for "EBR Subsonic Ammo" will produce many results of stores selling the product.
Extreme Shock also makes some, but I have no experience with it. It is also rather long and 100 grains, so I would be careful to make sure your barrel will stabilize it if you go that route.
Either way, factory subsonic .223/5.56 is rather expensive, and if he wants to play with some, he now has two leads. Youtube has videos showing both types, if he wants to see them in action before buying some. There you go Charles S., some information concerning the question you had asked.