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Butch & Co.Carlton, with your your permission, we'll re-post a couple of your pics of the plate, and re-pose the question, on the eBay collectors' forums, and see if anyone recalls the consensus there (it wasn't that long ago) or has any new insights. Unless you'd rather post to that forum yourself.
Dating a baseball artifact based on artwork is always a tricky proposition -- the artist may be inexpert with some details and rely on some artistic license -- but occasionally you can spot something that was clearly and definitively not in use until after a certain date, and that can at least give you a "no older than" figure. The left fielder in foul territory, for instance, is very probably just a compositional choice, but someone here expert in uniforms or equipment may recognize, say, the catcher's mask, as sufficiently detailed in the illustration to mark it as something from no further back than 1900, or 1910, or 1920.
The telling detail, however, is probably in the pottery marks on the underside of the plate. There's definitely something stamped into (not just onto) the pottery just to the left of the "Hand painted" inscription, although we can't quite make it out. Looks like an "infinity" symbol set at a 45-degree angle, but it's probably a flourish on some sort of monogram or logo. Can you tell what it is?