This paper proposes a vibration-based diagnostic methodology for aircraft bearings based on a joint first- and second-order cyclostationary analysis. The idea is to track the first- and second-order content over a predefined operating speed range, instead of ignoring the later or performing the diagnosis on an arbitrary stationary speed. The methodology applies to relatively long vibration signals recorded under strong speed variations, using a sliding window over which fluctuations are low. First, we obtain the time-evolution of the spectral statistics by computing the so-called instantaneous power and coherence spectra reflecting the first and second order content, respectively. Then, we design a time-to-speed transform based on fuzzy logic to transform the previously obtained time-cyclic maps into speed-cyclic maps, expressing the spectral statistics as functions of a predefined operating speed grid of interest. Last, we demonstrate the proposed methodology on a real vibration signal captured from an accessory gearbox of a CFM56 aircraft engine, with multiple bearing faults.