You can buy "blckboard paint" (which you can get in black or green). Depending on the board you wish to paint, you will most probably need to prime it first which can usually be done by painting with a coat of the paint thinned down with turpentine substitute if it's oil based.
As others have indicated, you should use special blackboard paint.
You need to paint it onto a smooth, non-absorbent surface. Just choose what is cheapest as long as it meets those two criteria (i.e. both smooth and non-absorbent). The wall-mounted blackboards used in many university lecture rooms (which are far, far better than those normally used in schools) are made of plate glass.
awww reminds me of when I was wee (even more wee than I am lol) and dad made me a blackboard, but it squeaked when chalking on it and set my teeth on edge haha