  We use our recent electric dipole moment (EDM) measurement data to constrain
the possibility that the HfF$^+$ EDM oscillates in time due to interactions
with candidate dark matter axion-like 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 $10^{-22}-10^{-15}$ eV. This is the first laboratory constraint on
the ALP-gluon coupling in the $10^{-17}-10^{-15}$ eV range, and the first
laboratory constraint to properly account for the stochastic nature of the ALP
field.
