If a time series is unevenly spaced, the simple moving average is not the best option to smooth it out (the window will be larger or narrower depending on the time distance of the events within that interval). Which method would you suggest that can be implemented when the time sampling of data is not constant?
The simple moving average can be considered as a weighted average of neighboring data points, where weights are 1 for data points that fall within the window and 0 for data points outside.
More sophisticated averages use triangular weightings. Or other kernels.
This suggests an analogue for irregularly sampled time series: use a weighted average of neighboring points, with weights that depend on how far these points are away from the time point you are averaging for. (This will also give you an interpolated value at a time point that you don't have an original sample for.) The weight function could again be triangular, for instance.