Hi Ronee! I always like to time my Walt Disney World visits during periods of lower park attendance levels too. You're right that Disney doesn't often offer discounts at the times of year where park attendance is at maximum levels.
March and April tend to be popular months to visit Walt Disney World since many schoolchildren and college kids have Spring Break during those months. Park attendance is typically at maximum levels during the week of Easter, which is in late April this year. Since Easter is later in 2014, the crowds may not be as high in mid-March. I like to consult the crowd calendars on unofficial websites like EasyWDW.com, which use factors like historical attendance data and holidays to attempt to predict park attendance levels. That site is predicting crowd levels during the week of March 15 to be a 7 out of 10, while the week of Easter is generally at 10 out of 10.
Early and mid-March would be a great time to visit Walt Disney World. You'll be able to take advantage of the spring
Special Offer discounts, and since park attendance won't be extremely high, you'll be able to experience lots of attractions without spending a lot of time in long lines.
Come visit us again here at the Moms Panel if you have more questions! We're always happy to help!