In this article by David Lundsford of the University of Minnesota Extension service I learned that Borax can be used as a spray to kill this pesky plant. Below is the dilution recipe and how to use it.
Borax Solution for Creeping Charlie Control:
Dissolve 10 oz. Twenty Mule Team Borax in 4 oz. (½ cup) warm water.
Dilute in 2.5 gallons of water.
This will cover 1,000 square feet. If you have a smaller area to treat, cut the "recipe" accordingly.
Apply borax when creeping charlie is actively growing in the spring, when no rain is expected for 48 hours. The borax treatment appears to be most effective during warm summers when soil moisture is ample.
Remember: The borax recipe has been tested only on creeping charlie and is not to be used on other broadleaf weeds. Be sure to use the borax spray only in the lawn because research shows established grass is tolerant of the spray. It should not be used in gardens.If creeping charlie is growing in a very shady location, think about what you can replace it with before spraying this borax treatment. Unless you can establish other plants you'll find the creeping charlie sprouting again in the same location.
Treatment can be applied only once each year for two years. If you still have creeping charlie problems, then switch to a standard herbicide.
To read the entire article click here. http://www.extension.umn.edu/yardandgarden/ygbriefs/h519borax.html
For more about the backyard Gardners here is the link http://www.freeplants.com/