What a great question!
First. Yes, There are such a thing as “Black Moons”, which are new moons with the “Blue Moon” Rules applied to them. ( http://en.wikipedia.org/wiki/Black_moon ).
The March 15th New Moon would not be a “Black Moon” as per the “Sky and Telescope Rule”. The S&T Rule would be the 2nd New Moon in a calendar month. For this to happen one has to look for months where the new moon occurs on the 1st of the month so the second new moon (29.5 days later) can appear in the same month. A March 15th New Moon could not do this.
For the “Maine” and “Astronomical Season” Rules (The third new moon in a season of four new moons), the new moons for 2010 are as follows.
Winter Solstice December 21, 2009
January 14 New Moon
February 13 New Moon
March 15 New Moon
Vernal Equinox March 20, 2010
April 14 New Moon
May 13 New Moon
June 12 New Moon
Summer Solstice June 21, 2010
July 11 New Moon
August 9 New Moon
September 8 New Moon
Autumnal Equinox September 22, 2010
October 7 New Moon
November 5 New Moon
December 5 New Moon
Winter Solstice December 21, 2009
As you can see, there are no seasons in 2010 with 4 new moons in them. So there are “Black Moons” but none occur in 2010.
Hope this helps.
Tom