I noticed that many trikes have a basket in the back but I need something much stronger capable of carrying a golf cart battery which weighs about 60 pounds so is that possible to make a custom one capable of that weight or even better, capable of carrying 2 of those batteries simultaneously for 120 pounds total? Could it just be made out of wood or is metal better? Do you think having that much weight back there would cause any issues such as frequent flats on the rear tires unless I use super thick tubes?
I'd use a trailer for this. There are ready-made ones like http://www.bobgear.com/bike-trailers or you could build your own. Then a lot of the weight can go onto a dedicated trailer wheel (or two), which should make it no big deal to carry two 60 pound batteries (assuming you have legs of steel, obviously).