What are the requirements to make the white "treasure" ships (which lead to airship levels full of coins) appear in Super Mario Bros 3? Can I make them appear intentionally?
To make a Hammer Bros. turn into a coin ship:
Each second left on the clock gives you 50 points. That means you should end with an even number of seconds left on the clock if you have a score ending in 10. If you have a score ending in 60 you should finish with an odd number of seconds on the clock. Anything else and you're out of luck!
There are also white mushroom houses that appear if you get every coin on a particular level in each of the first 7 worlds:
1–4: 44 coins 2-2: 30 coins 3–8: 41 coins 4–2: 22 coins 5–5: 28 coins 6–7: 78 coins 7–2: 41 coins
I am assuming you mean turning a wandering Hammer Bro into a white treasure ship. From Gamespot: