We had my 19 mth old triplets iron tested because 2 out of the 3 were eating wood! Chewing baseboards, gates, dressers etc. We knew they could have low iron b/c they were preemies & had already been supplemented as infants. I'm not sure the best way to go about getting more iron in their diet or if the OTC iron supplement I bought is the best absorbed. Worried of course about causing constipation.
Iron supplementation in 19mth olds
When you had them tested, what were the results? You'll probably know what treatment to pursue based on how iron-deficient they are, and their doctor will have suggestions.
Some supplements are hard to get into toddlers -- they can taste really bad. My 3 year old has to take a supplement and we had a lot of trouble finding one we could get down her. We use Nature's Plus Chewable Iron with Vitamin C now and she takes it without a fuss. But again, to know how much to give them, or whether you need to supplement or can use Floradix or foods higher in iron really depends on what their levels are.
There are some good ways to get more iron into the foods they eat, too. Some of them are surprising (like edamame, coconut, blackstrap molasses) and some are the usual suspects (lean red meat).
I'd look into whatever their doctor suggests but one of the things we do in our family (I tend to be anemic, and DS was around 9 months) is cook most things in cast iron skillets. The iron in the skillet is absorbed a bit into the food--especially if you cook acidic stuff in them (like tomatoes), it destroys the "seasoning" on the pans, but does increase iron content in the food.