Like most airgunners i tried cold blue solutions which gave poor results, streaky non durable coating etc. I also tried birchwood casey plum brown stuff, this gave an interesting colour on a plai iron barrel but i suspect it was no more durable than the cold blue stuff.
I bought Angiers book & it has loads of good info though obviously written aeons ago so much is out of date.
One day at Bisley arms fair i bought some real browing solution from Blackleys, It gave proper real results on an antique damascus pistol barrel.
It also gave good results used as a blue the only difference being that i boiled it after each pass, the boiling converts the ferrous oxide to black ferric chloride. The main reason for any problems is poor degreasing.
A bottle will last you years, its highly poisonous as its got mercuric chloride in it, dont use it anywhere near anything you dont want to go rusty!
Link here,
https://www.blackleyandson.com/acata...Metals-p1.html,
Ignore the birchwood casey snake oil crap, scroll down to gunguard slow brown.