You should definitely look beyond the fruit and vegetable group to identify foods that you can give your child. Certain grain products have very high levels of iron, even higher than some meats. Cream of wheat, for example, has more iron in a serving than beef liver does! Brewer's yeast and molasses both have very high levels of iron, and can be used in preparing other foods. Enriched rice and oatmeal also can have substantial amounts of iron.
In order to get the best mileage out of any iron-rich foods you are giving, it is helpful to also give a food that contains Vitamin C along with the iron. Vitamin C helps the intestine to absorb the iron more effectively. If the iron doesn't get absorbed, it just ends up going out in the stool. Some foods are known to interfere with the absorption of iron from the intestines, and it is helpful to not give these foods at the same time if you want to maximize the amount of iron that's absorbed from the meal. Milk in particular is known to interfere with iron absorption. This doesn't mean to stop giving your child milk -- just don't give the milk at the same time as an iron-rich meal.