However, a dedicated SXS clays gun seems to be less popular with shooters and hence with many manufacturers too.SKB perhaps manufactured the first SXS clays gun and they still make one.
http://www.skbshotguns.com/Shotguns/M200HR.php
https://skbshotguns.com/side-by-side/385.php
While I was searching, I found this gun. I think this is a very well made gun though I would like the beavertail forend trimmed a bit.
Photos and texts from here.
Here's a nice Side-by-Side shotgun that was manufactured in limited numbers. This is an SKB Model 385 Sporting Clays Set. This set includes a pair of 20-gauge and 28-gauge barrels which are both serial numbered to the receiver. Both sets of barrels measure 30" in length and are equipped with high ventilated rib, Hi-Viz front sights w/ mid beads, and screw-in chokes. The 20-gauge barrels have 3" chambers, the 28-gauge barrels have 2-3/4" chambers. The gun is equipped with a single-selective trigger and automatic ejectors. The safety has been made non-automatic but the original parts are included to return it to automatic function if desired. The receiver is engraved and features a durable silver nitride finish. Overall condition is excellent and the metal finish rates 99%+ with very slight handling wear but no dings, scratches, rust or pitting. The stocks show a few small marks (a couple marks to the left side of the butt and a couple marks to the right side of the 28-ga forend). There are no cracks or chips. LOP measures 14-1/8" over the black Old English pad. Drop @ Comb is 1-1/2"; Drop @ Heel is 2-1/2". The mechanics appear to be in perfect working order and the bores are bright. It comes with several choke tubes: 20-Ga extended IM, M, IC, SK I, SK II; 20-Ga flush M, IC, SK; 28-Ga flush MOD, IC, SK, SK, SK. A choke wrench and extra front sight inserts are included as well. The set comes in the factory case that is in very good condition. According to the information I have found, something between 50 and 200 of these sets were produced between 1999-2004.
Best-
Vikram