Tom,
You're correct Browning discontinued the scope mounts when they discontinued the BPCR's. If you search far and wide a set of Browning bases can be located. They're likely be pricy. But Weaver has bases that will work. The following is a from the section on scope bases from the book material I writing on the Browning BPCR.
Wayne
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Weaver also offers bases, which will fit the Browning BPCR. They are listed for the Browning 1885 High Wall (octagon barrel) with the following cautionary note, SHIMMING IS PROBABLY REQUIRED FOR PERFECT SCOPE ALIGNMENT. Weaver model #11 base is for the rear and model #29 base if for the front. I can confirm the Weaver bases will fit and shimming is definitely required on my rifles when using standard Weaver rings. Shimming totaling 0.038 was necessary under the rear base for perfect scope alignment. I have not tried them but I understand Weaver style Burris Signature Ringsâ alone, or with Burris Signature Pos-Alignâ Offset Insert Kit, will eliminate the shimming and provide addition elevation or windage adjustments if necessary.