We constrain the coupling between axionlike particles (ALPs) and photons, measured with the superconducting resonant detection circuit of a cryogenic Penning trap. By searching the noise spectrum of our fixed-frequency resonant circuit for peaks caused by dark matter ALPs converting into photons in the strong magnetic field of the Penning-trap magnet, we are able to constrain the coupling of ALPs with masses around 2.7906-2.7914 neV/c2 to gaγ<1×10-11 GeV-1. This is more than one order of magnitude lower than the best laboratory haloscope and approximately 5 times lower than the CERN axion solar telescope (CAST), setting limits in a mass and coupling range which is not constrained by astrophysical observations. Our approach can be extended to many other Penning-trap experiments and has the potential to provide broad limits in the low ALP mass range.