We use our recent electric dipole moment (EDM) measurement data to constrain the possibility that the EDM oscillates in time due to interactions with candidate dark matter axionlike particles (ALPs). We employ a Bayesian analysis method which accounts for both the look-elsewhere effect and the uncertainties associated with stochastic density fluctuations in the ALP field. We find no evidence of an oscillating EDM over a range spanning from 27 nHz to 400 mHz, and we use this result to constrain the ALP-gluon coupling over the mass range . This is the first laboratory constraint on the ALP-gluon coupling in the range, and the first laboratory constraint to properly account for the stochastic nature of the ALP field.