The vibronic (vibrational-electronic) interactions and Jahn-Teller distortions in the mono- and trianions and the mono- and trications of coronene are discussed. E-2g modes of vibration remove the orbital degeneracies in the highly symmetric D-6h molecule to lead to D-2h distortions. We calculate and analyze the vibrational modes and the linear vibronic coupling constants of the anions and cations of coronene as well as its deutero-form using the (Becke and Lee, Yang, and Parr) density-functional method. Although there are twelve E-2g modes of vibration in coronene, some of them appear to play a significant role in the Jahn-Teller distortions. The lowest frequency mode of 370 cm(-1), the C-C stretching mode of 1668 cm(-1), and the C-H stretching modes of 3177 and 3193 cm(-1) give large coupling constants in the anions. In particular, the 1668 cm(-1) mode plays the most important role in the Jahn-Teller distortions both in the anions and cations. There is electron-hole symmetry in the coupling constants in the anions and cations. We also demonstrate an important H/D isotope effect. The highest two C-H stretching modes are important for the Jahn-Teller distortions in coronene; however, the corresponding C-D stretching modes are less important for the Jahn-Teller distortions in deutero-coronene.