The coconut milk in the dairy/milk section does have carrageenan in it. But if you go to the Asian section, they sell cans of coconut milk that does not have carrageenan in it and is really good! I have been using that in my coffee and also adding a little bit to my smoothies to give it a more creamy taste.
Theres a Silk Brand that is non dairy there is also a rice milk they are reasonably priced and you can find them in Publix and Sweet Bay
Rice milk and almond milk are very good. But just don't forget, if you are not on dairy you need to up your calcium elsewhere. Almond is high in calcium but you may need more than that to keep levels good.
Many non-dairy creamers contain corn syrup which is not a good thing!
Try almond milk. It tastes better than regular milk.