What you are talking about is called a "cover crop." Some cover crops are planted in the spring, some fall; some need two crops per year, some need mowing, etc. Your requirements seem to be a spring-planted crop that keeps out weeds with little or no work until you replant your garden next year. Below I have listed possibilities for you that can be treated as annuals. Please refer to the following Web site for further information:
http://www.extension.umn.edu.projects/yardandgarden/ygbriefs/H234greenman.html

Also, information on clovers can be found at:
http://www.agry.purdue.edu/forages/publications/legumes/white_dutch.htm

Clovers
a. Dutch white - 6 to 8 inches tall and Ladino 10 to 12 inches tall. Both are drought intolerant and do not do well on sandy soil.
b. Hubam sweet - does well on poor soil.
c. Mamouth red - 1- to 2-feet-tall.

Hairyvetch - This is the most effective soil builder on sandy, well-drained soil but needs a fall planting.

Peas and beans - A shelling bean with a longer season to have it mature in your area in the fall is a good cover crop but does not keep out all the weeds. I did this one year and found it satisfactory. I also picked the bean pods, but you do not have to.

Each of these cover crops needs an inoculant to fix the nitrogen in the soil. This inoculant is sold separately.

These cover crops do not add measurably to your garden's other nutrient needs such as potassium and phosphorus.