Preheat oven to 350 degrees Fahrenheit.
Beat together applesauce, sugars, margarine, peanut butter and "eggs" until sugar is dissolved. Add vanilla. Combine flour, baking soda and salt by stirring it into the mixture. Mix in oatmeal until just combined. If the batter is too wet, add more oatmeal. Drop tablespoonfuls onto ungreased cookie sheets. You can also use parchment paper. My mother-in-law uses a tablespoon dropper and it works really well.
Bake for 10 to 15 minutes until light brown.
Source of recipe: This recipe was modified from this one: http://allrecipes.com/Recipe/Oatmeal-Peanut-Butter-Cookies/Detail.aspx [1].