Finding the period of a noisy oscillating signal

I have a stochastic simulation of an oscillatory system, so the signal is pretty noisy. Any ideas for getting the period of the oscillations would be helpful.

I can't use the power spectrum (fft) because the simulation is based on the Gillespie method (indep sample times come from Poisson dist), so the sampling frequency isn't constant. At least I think this is why fft isnt working.

I can't use a butterworth filter + peak detection because the filtering affects the location of the peaks.

Ideas? Thanks

edit: I ended up using filtfilt to apply a Butterworth filter, as suggested by someone in r/math. If you aren't familiar with filtfilt (I wasn't), it's actually a pretty useful function that applies a filter once forward then once backward on the filtered data in order to get filtered data without a phase shift.