The problem isn't your bow, but your arrows. As was mentioned above, put more more weight up front on your arrows. This will produce the effect of less spine (i.e. resistance to bending) on the shaft. That's important because when shooting a non-centershot bow like you've got, proper arrow spine is critical. If you don't understand archer's paradox, do a short search to learn about it. Centershot bows are more forgiving of various spine weights since the arrow isn't forced around the handle nearly as much. Don't fall prey to the myth that bows with shelves shoot more accurately than bows without them...it's all a matter of proper arrow tuning.
If you don't have any heavier points for your arrows, which I assume are wood, then you can add brass tubing to the ends to up the weight. You can get it at local hardware stores. Here's a picture of mine:
A little hot melt or superglue will hold them in place. I wouldn't cut a rest into your bow. Here's a picture of a red oak pyramid bow I did some time ago with a leather floppy rest. The bottom picture is a 15 yard group out of that bow with properly matched arrows.
Best us luck, and be sure to do a search on archer's paradox. While you're at it, do some research to better understand arrow spine and how it affects arrow flight.
There's lots posted on these subjects on this site and others.
