For anything H&R related, you should check out Graybeard Outdoors message boards. They have a great deal of information on these guns and how to make them shoot. I have had lots of luck with all of mine thus far, my 45-70 is the most accurate Handi i have.

Before i went about putting another new scope on it i would read the FAQ and help posts on the GBO. Off the top of my head rest the rifle on the frame just in front of the trigger guard. Also take off the the front stock and shoot it that way, if that makes the gun shoot better then you will need to address that issue.

http://www.go2gbo.com/forums/index.php/board,126.0.html