The convention is to use 4 digit years after the year 2000... so any 2 digit years it assumes are from the 1900's.
You say that the year 11 should logically be 2011, but that isn't true if you are asking for a birth date. Also consider all of the years where the year 11 logically meant 1911... it was like that untill the great Y2K scare. Since nobody wanted to go back and correct all of the dates in the past, the solution is to always use a 4 digit date moving forward.
My best suggestion is to use a 4 digit date and to require one. The only other solution would be to create a custom script that parsed the entered date as a string and converted 2 digit dates to 4 digit dates automatically, but we don't supply that code so it would have to be custom written.