You can buy all kinds of brackets for boats but the most common and easy kind attaches to a stainless steel
rail on the boat and the photo
you show has no rails at all.
You can find other kinds of brackets that start with a flat plate that would attach to the back or side of the boat. You might be tempted to use screws to attach it but that is not very strong and will probably pull out, sooner or later. It is better to find a spot where you can reach both sides and use a nut, bolt and washers to attach the bracket.
You could shop for marine
BBQs and some might offer different mounting options or go to a boating
store to see what kind of general purpose brackets they offer that might work.
This looks like a boat that you would use in a lake, river or bay where you would be close to land. Why not take a grill
along and just set it up on the shore or beach?