Ken, you are basically creating a short, smooth bore muzzleloader when you make a small cannon. So, you will want to use the same things as a muzzleloader. Many people mistakenly think they can use any old powder and that any idiot can figure out how to pour powder into the barrel and ram a ball down on top of it. Believe me, it is not that simple. Entire books have been written on the subject. I highly recommend that you get some instruction from someone that is very experienced with muzzleloaders. There are dozens of variables when creating a load, and dozens of things that can go wrong. For your own safety, please seek out proper help. I can help you with some basics, enough to get you started, but to teach you everything that I typically teach to others would require you to make a trip to Minnesota for some serious range time. I am nationally certified to teach muzzleloading through 4-H and the NMLRA, so yes, I could teach you, but you will just have to trust me when I say that you would be best off to get some hands on instruction from someone who is genuinely knowledgeable on the subject.
To figure out the bore, obtain some of the steel balls that you plan to use. Let's assume that they are exactly .250" in diameter. You will need to allow for a cotton patch to fit between the ball and the bore because the patch wraps much of the way around the ball. Patches are commonly available in .010" as well as some other thicknesses, but .010" are probably the most common. So, add one patch thickness to the diameter of the ball (.010 + .025 = .035") arriving at a desired bore of .035. You might think that it should be .045, but the patch needs to compress a little bit, which is why we only make the bore .035".
If you prefer to shoot .22 caliber pellets, do this: purchase a .22 caliber rifled sleeve from Brownell's, then machine your cannon bore to accept the sleeve using a good firm press fit, or better yet, make it a shrink fit. If you shoot pellets, you will not need any patches, more about that shortly.
What do you plan to use for powder?? This is an important consideration. If you are going to use black powder, such as Goex or Swiss, you will want to use FFFg (3F). If you are going to use black powder substitutes, such as Pyrodex, you will want to use 'P' type, which is similar to 3F. If you use Triple 7, American Pioneer, Shockey's Gold, or Black MZ, you will want 3F. Next question is how much powder to use. Keep in mind that it is very important that you ALWAYS use a powder measure of some sort, never pour powder from your container directly into the barrel. From experience I can tell you that 7 to 10 grains (by volume, not weight!) will be great plenty when using any of the powders listed above. Ten grains of 3F will give you consistent shots with a .22 caliber pellet at 50 yards. If you use Triple 7, use 10% less as listed in the instructions that come with the powder. One last note on powder: NEVER USE FFFFg ( 4F ) POWDER AS A MAIN CHARGE. And I mean NEVER! Period. Don't do it. Powder that fine creates dangerously high pressures when it burns in a confined space. Also do not be tempted to use modern smokeless powders.
When you load, measure then pour in your powder first, then center a lubed patch over the muzzle, and place a ball over it, then ram the ball and patch down on top of the powder. No need to ram it hard or hammer it down, just press it down firmly on top of the ball. MAKE ABSOLUTELY CERTAIN THAT THERE IS NO AIR SPACE BETWEEN THE POWDER AND THE PATCH AND BALL! If you use pellets, you will not need to worry about the patch, just your powder and then the pellet. The no air space rule applies for pellets, too. Also make absolutely certain that you do not accidentally double charge the bore.
When black powder burns, it leaves behind some residue that builds up inside the barrel just above the point where the ball or pellet rests on the powder. This residue will build up very quickly in a small caliber piece, and can cause the ball or patch to stop short of the powder when you ram it home. This will cause an air gap between the powder and the projectile, which when ignited, has the same effect as an obstructed barrel. In a mild case, and obstructed barrel or an air gap will 'walnut' or bulge the barrel. In a worst case scenario, the barrel could explode. To prevent this from happening, you will want to run a damp cleaning patch down the barrel after every shot. Not wet, just damp. This serves the double purpose of removing the powder residue as well as extinguishing any smoldering embers that might remain in the barrel.
I could go on and on, but what I have provided here is enough to get you started. Have fun, but be safe, and seek out some good help. If you choose to ignore any of the warnings given here, all I can say is that it has been nice knowing you.