H&R offers a good selection of accessory barrels for the Handi-Rifle but if you don’t see what you’re looking for, you can get a custom barrel.
There is only one gunsmith that I know of that makes custom barrels for the H&R Handi-Rifle. His name is David White and his website is D and T Custom Gun Works. David is a master gunsmith with the H&R Handi-Rifle and the T/C Contender and Encore. He also does other custom gun work.
David White uses a process called Barrel Stubbing to produce super accurate barrels for the Handi-Rifle. The barrel stubbing process uses a short barrel stub with the barrel lug and is bored and threaded to accept another threaded barrel. This eliminates the barrel stress in the chamber area during the lug welding process. The barrel has no stress because it has not been welded.
I have read many reviews on his forum and on the web. He is nothing short of spectacular. He is the best there is when it comes to the Handi-Rifle, T/C Encore and T/C Contender.
David White’s barrels are not cheap but if you want the best then he will give you that.