Not really a nickname so it doesn't have the clear cut proper noun usage. I believe when referred to as a third party it wouldn't be capitalized, e.g.
"My old man is turning 70 this year!"
But how about when directed at the father himself?
"You're about to turn 70, old man!" "Hey Old Man, where's the screwdriver?"
Using old man for their own dad is often disrespectful and not that common to begin with, but it does happen. So how should it be capitalized?
Examples where you would capitalize "old man":
When part of the name someone is known by:
Old Man McCourt, Old Man Hodges, etc. (but be careful about using the "nickname" as part of direct address)
When part of the official name of something:
When part of a title:
The Old Man and the Sea by Ernest Hemingway
"Old Man" by Neil Young.
Note that you will always capitalize "Old" at the beginning of a sentence, but "man" will not necessarily follow suit.
Examples where you would NOT capitalize "old man":
When you are simply applying the adjective old to the noun man:
James lived to be a very old man.
An old man should have acquired wisdom from his many years of life.
When you are talking (informally) about a father or a husband:
Have you seen my old man? He said he was going to meet me here.
When you are using direct address:
Hey, old man, your daughter is looking for you.
Old man take a look at my life / I'm a lot like you were
We capitalise proper names, and nicknames, but not terms of endearment (e.g. "honey", "son", "pal", etc), so if he is formally or informally named "Old Man", then it would be capitalised, otherwise not.
