This is called load development. Your rifle will the best source to learn the best accuracy. Measure the bore to determine the bore diameter. An old Dixie Gun Works catalog from 1975 (?) might have bore diameter. The ball suggestion would be 0.010" less than the land to land bore diameter with a patch having a modest compressed thickness of the groove depth. All of these measurements can be determined by an inexpensive digital caliper capable of inside and outside measurements.
Choices listed in my copy of a 1977 edition of the "Black Powder Gun Digest 2nd Edition" simply lists caliber of the Tingle M1962 rifle being 36, 45 or 50 caliber with a 1 in 52" twist. Ball size, I would suggest a 0.440" or 0.437" ball. Patch thickness of 0.015" or a little thicker. Lubricant is your choice from spit, olive oil (or any cooking oil), a mix of Ballistol 1 part to 7 parts of water, GoJo hand cleaner (no pumice) or a commercial lubricant. since the rifle ha a fairly slow twist, a starting powder charge of 50 grains of 3fg to increase at 5 grain charges until you get your best group.
You can buy the Dutch Schoultz Accuracy system at blackpowderrifleaccuracy.com for about 94 pages of instruction of how to get the best accuracy from your rifle.
I too have a Tingle 45 and mine looks like Cowboys except the lock is on the wrong side. I've only shot it a few times, but I used a .440 ball too and a pillow ticking patch is a tight fit with a Dutch's 1-7 dry lube patch. I haven't shot it more than about a dozen times, but it seems quit accurate without having really worked up a load. I think I just used 50 grains of 3f. Mine shows much more wear than Cowboys but is a neat rifle. I'm a righty shooting this left handed rifle out of sympathy for all our left handed friends. I had thought of selling it, but have two right handed daughters who are left eye dominant and also have a lefty grandson.