A: I have struggled with the same issue for my son, who is gluten free and can't tolerate most kids vitamins that are sweetened with sugar. Right now we use a product by Thorne Research that was recommended for my seven year old by a nutritionist. It is called Cal-Mag Citrate (Effervescent Powder) but it is very, very sour because of the high vitamin C content and I WOULD NOT recommend it for a one year old. But, what I would recommend is the combination of calcium and magnesium in the evening. Both these minerals are down regulators and taken together they help kids to sleep and be calm. I was actually in a store today looking to replace the Cal-Mag powder with something similar which didn't contain the vitamin C--so this was on my mind before I received your question.
Doing some research, it looks like TACA recommends a calcium powder by Kirkman. They have several available, but the Calcium with Vitamin D Powder-Unflavored-Hypoallergenic looked the most similar to the Thorne Research product, which my son seems to do well on. 1/4 tsp of this product would provide 500 mg. of calcium. You can order small samples from Kirkman, to see how well your child does with the supplement before you order. And the sales people at Kirkman are very knowledgeable and can give you more information.
My son has reacted poorly to several calcium supplements. I thought it was the calcium but really it turned out to be the sucrose (in the gummy calcium) and the preservatives and stevia (in the liquid New Beginnings Product.) So while the liquid vitamins might seem easier to use, very sensitive kids sometimes can't tolerate them because of the preservatives and what they put in the products so they don't separate . In addition, there are some kids who don't do well on calcium at all and there are some kids who do better with one form of a vitamin and can't tolerate another form, so observing how your child does on a new supplement is really important.
Here are the recommendations for calcium intake according to the Surgeon General I found in an article in the Seattle Times called Calcium is Critical--Especially for Kids:
Children 0-6 months: 210 mg
Children: 6-12 months: 270 mg
Children: 1-3 years: 500 mg
Children: 4-8 years: 800 mg
Children: 9-18 years: 1,300 mg
Adults 19-50 years: 1,000 mg
Adults 51-plus 1,200 mg
Because the ratio of calcium to magnesium is important for the absorption of calcium, it is also critical to make sure you have enough magnesium when you are taking calcium. This is of special concern for kids who have signs of being deficient in this mineral. Sensory issues, constipation, hyperactivity and allergies can all indicate low levels of magnesium. Kirkman has a Magnesium Citrate Soluble Powder which is also hypoallergenic. There is also a Kid's Calm product for ages 4-8 although it is very sour and also contains stevia and flavoring.