I am not sure if this qualifies as auto-calibration, but you can estimate the fundamental matrix from two images by matching points using the estimateFundamentalMatrix function. See the Uncalibrated Stereo Rectification example.
You can also calibrate without a checkerboard, but you would have to do that programmaticaly, rather than by using the app. The estimateCameraParameters function takes image points and the corresponding world points. These points can come from any planar reference object, so you can use circles or any other calibration pattern. This also means that you would have to provide your own code for detecting this pattern in the images.
