Again this is a relatively simple process for which there are two ways to proceed.
1. Have it done professionally. If you don't know a gunsmith simply Google 'Barrel Blacking' and a load of very capable people will come up.
2. If you don't mind a bit of hard work use 0000 wire wool remove ALL traces of the previous blacking and then use one of two sets of substances:
Barrel Blacking Kit from Caswell Europe (1 Litre "SD Cold-Ox" kit costs £19.95 +P&P and the 1 litre kit is plenty to do several barrels and other metal parts).
Perma Blue Kit from Birchwood Casey (or similar) and can be found by a simple Google search an costs about £10 with the P&P.
When this is done you may wish to 'age' the metal work with some 0000 wire wool. I would suggest looking at another example of the weapon to see where the wear marks are.
If you are doing the DIY method when you are using the chemicals use gloves as you are likely to leave oily finger print marks all over your project!