Carbon is not a form of coal. The opposite is more nearly true. Coal is a sedimentary rock that contains a large percentage of carbon, but also contains water and impurities. Coal was formed from plants, which contain a high percentage of carbon, making coal an organic substance. The confusion of your students is common.
Many people talk about compressing coal into diamonds.
However, it is graphite, a form of carbon, that is compressed to make industrial diamonds. Argonne National Laboratory, Division of Educational Programs, Harold Myron, Ph.D., Division Director.