Conversion of Langleys

How do I convert Langleys per day or per minute to Joules per cm2 per day? I know 1 langley = 4.184 J/m2, but how do I incorporate the time measure?

You may want to check that. This site gives a VERY different conversion.
http://www.unc.edu/~rowlett/units/dictL.html

langley (Ly)
a CGS unit of heat transmission equal to one thermochemical calorie per square centimeter, or exactly 41.84 kilojoules per square meter (kJ/m2). Named for the American astronomer Samuel P. Langley (1834-1906), the langley is used to express the rate of solar radiation received by the earth.

Nothing really wrong with joules/day as a measure of total energy received from the sun. If you had langleys/minute, I would convert to langleys/second, and then recognize that a joule/second is a watt.