So possibly via applescript.
You may want to check over in the Photoshop Scripting Forum
but I guess most of the regulars don’t bother much with AppleScript.
AFAIK that's stuff only filters can do. One would probably sample columns/ rows or randomly angled lines and process their histogram to find the middle between some "peaks". Averaging multiple such results would then provide a center point. Additional processing could also eliminate any appendages that would skew the result. Of course this could be amped up indefinitely e.g. by calculating the gradinet vectors based on thresholds and finding the center that is farthest away from any "edges" or detecting the densest samples in DCT transforms or whatever. A million ways to go about this, but definitely beyond simple scripting or actions.
the nearest I think I could get,
Copy to clipboard the entire layer
Crop the vertical by half, with anchor point bottom centre,
Trim based on transparent pixels
From this you should have the centre point of the bottom half of the image, then some how replace from the infomation in the clipboard.....