30 / 9 / 2137
is Monday 14 RamaDHaan 1562 A.H.
I was born on 30/9/1974 or Monday 14 Ramadhaan 1394, according to most calculations.
It is expected to take 163 Gregorian years or 168 Hijri years until my birthday anniversary would fall on the same date in both calendars once again. Interestingly, the days of the week coincide also.
But, this year and next are about as close as I would get in my lifetime to the two falling on the same date. The cycle of near-alignment repeats every 32-33 years. So, if I were to live to be 64-66, there is another near alignment in which the two birthdays fall in less than 10 days of each other.
http://www.rabiah.com/convert/convert.php3 - you can play with this converter and see when your birthday was and when they might align again. I tried a different date and tried 163 years and it was two days off, so 163 years would not work for every pair dates, but it gets close.