The MAXIMUM that you can use is: 51.
Vitamins give EVs, which a Pokemon can only have 510 of. Also, You cannot use more than 10 of 1 kind of Vitamin per stat. There are 6 Vitamins, meaning there could be 60 uses, but 510 is the maximum.
Meaning something like:
10 HP up+10 Carbos+10 Protein+10 Zinc+10 Calcium+1 Iron=51 Vitamins
But you cannot:
51 HP up
10 HP up+10 Carbos+10 Protein+10 Zinc+10 Calcium+10 Iron