I'll give this a shot.

The chance of getting a royal flush in diamonds when you take 7 cards is 0.000808016%. So the chance of getting a royal flush in any suit is 4 times that or 0.003232062%.

The chance of that happening at least once when you do it 7 times is 1-(1-0.00003232062)**7 or 0.022622241%.

Or once in 4,420 hands.