I have kept tiger barbs and cories together with no issues. That being said...it really is dependent on the fish. I would get the largest cories I could find. Minimum would be 4 to a group. A group being the same kind...all bronze or all albinos or whatever. they will school with different kinds, but will be happier if it is all the same. I would add the cories all at the same time. Strength in numbers...they will feel safer. Provide them with plenty of cover...but I think it would be fine. If you keep up with water changes, I think you could add 2-3 more barbs. I would add them at least a week if not a little longer after you add the cories.
I think you will find the barbs will not even notice the cories.