People with felony convictions are allowed to fish, absent some kind of special provision imposed by a court or other authority. For example, convictions for certain fish/wildlife crimes can result in loss of fishing privileges for specified periods of time. Make sure your buddy/cousin doesn’t fall into this category.
I believe felons can also possess a bow, but there can be restrictions. In North Dakota a bow/arrow is defined as a “dangerous weapon”. Felons under active parole/probation supervision are typically not allowed to possess dangerous weapons, thus no archery gear while under supervision. It’s possible a felon may have their right to possess any dangerous weapon restricted for a set period of time ( 5 years, ten years etc.) as well, separate from any parole/probation, depending upon what state law outlines and what was imposed at the time of sentencing.
I’m guessing your cousin will be just fine to go out fishing. I’d recommend he call Game and Fish before messing with a bow/arrow, just to be on the safe side. Hope this helps!