Strategies to produce an ultracold sample of carbon atoms are explored and assessed with the help of quantum chemistry. After a brief discussion of the experimental difficulties using conventional methods, two strategies are investigated. The first attempts to exploit charge exchange reactions between ultracold metal atoms and sympathetically cooled C⁺ ions. Ab initio calculations including electron correlation have been conducted on the molecular ions [LiC]⁺ and [BeC]⁺ to determine whether alkali or alkaline earth metals are a suitable buffer gas for the formation of C atoms but strong spontaneous radiative charge exchange ensure they are not ideal. The second technique involves the stimulated production of ultracold C atoms from a gas of laser cooled carbides. Calculations on LiC suggest that the alkali carbides are not suitable but the CH radical is a possible laser cooling candidate thanks to very favourable Frank-Condon factors. A scheme based on a four pulse STIRAP excitation pathway to a Feshbach resonance is outlined for the production of atomic fragments with near zero centre of mass velocity.