What is the average monthly birth rate in US?

The US Government tracks birth rates per year. "As of March 2011, births fell 4% from 2007 to 2009, the largest drop in the U.S. for any two-year period since the 1970s. Births have declined for three consecutive years, and are now 7% below the peak in 2007".

Data for United States in 2009

Number of births: 4,130,665

Birth rate: 13.5 per 1,000 population

See the link below for U.S. National Center for Health Statistics through June 2011, published February 2012.