Due date to pay quarterly estimated tax for 1099 contractors

The 15th day of the 4th month of your fiscal year,
The 15th day of the 6th month of your fiscal year,
The 15th day of the 9th month of your fiscal year, and
The 15th day of the 1st month after the end of your fiscal year

Source : http://www.irs.gov/publications/p505/ch02.html#d0e6025