While it's possible that your hair is truly coarse, some people with curly hair think it's coarse when it's really just dry. Here's a link from CJ Marsha's blog Curl Junkie - Natural Hair Care for all types of Curly Hair!: My 2 cents on Protein/Texture/Porosity/Moisture Balance! :-) that has visuals. This will also give you some ideas of where to start.

My hair isn't coarse, it's low porosity. It prefers the more natural products from the online, boutique type companies. Curl Junkie conditioners are really moisturizing, as are the deep treatments (Curl Rehab and H & B Deep Fix.) The Marie Dean products are all richer and she has a lot of conditioners, DTs. Kozama is has a lot of moisturizing products.
3a (Corkicelli), highlighted, fine, low porosity

HGs: Anything Sevi; Curly Kinks Satin Roots, Curlycue ReNew and Coil Jam; homemade FSG and okra gel; soap bars; UFD Curly Magic; Botanical Spirits Jellies, CJ Repair Me, Aloe Fix