Here's one I built in my backyard about 7 years ago.
View attachment 367301View attachment 367302View attachment 367303View attachment 367304
It's overall design is similar to the BBQ pits in the city parks in St. Louis (my hometown). I updated it so I could have my choice of a charcoal smoker or a propane grill. Bought the grills on sale at Home Depot.
I used cinder block for the main structure to keep the cost down. However, if you want a more standard type of charcoal pit with steel grates for the food and the fuel, you could use firebrick or maybe even common clay brick and modify the design so you have access to the grates through a hole in the side opposite the chimney.
The facing is stone (drain rock used in septic system leach fields) set in mortar--very inexpensive. Smoke from the charcoal smoker is directed out the chimney. There's a spark arrestor screen near the output end of the chimney.
Good luck