Dielectronic recombination (DR) is the dominant recombination mechanism at coronal temperatures and densities. We present a procedure for calculating DR rate coefficients as a function of electric field strength and apply this method to carbon ions. We focus on the competing effects of enhancement by plasma microfields and rate decrease through collisional excitation and ionization. We find that, in the case of C(3+), a significant rate enhancement results, leading to a reinterpretation of C IV emission-line intensities in the sun and late-type stars. We further consider how macroscopic electric fields, in particular motional electric fields, can affect DR rate coefficients, demonstrating dramatic rate increases for a number of the carbon ions.