The vast majority of Target and Live Bird guns using 1 1/4 oz. in the U.S. in the 1870s were 10b
January 3, 1878 Capt. A.H. Bogardus broke 5000 glass balls at 18 yards rise in 10 hours 40 minutes 35 seconds, missing 163, using a 10b W&C Scott with 3 1/2 dram 1 1/4 oz. 8s.

Jan., 1879, The Chicago Field
Jamaica Plank Rd., L.I., New York
Brooklyn Gun Club vs. Philadelphia Gun Club, 8 guns per side. Only two Parker guns on the grounds. Mr. T.E. Broadway of the Brooklyners used a Parker 10 ga. with close choke weighing 9 1/2 lbs shooting 4 1/2 drachms of DuPont's Diamond Grade and 1 1/4 oz of Tatham's soft shot. For the Philly club, Mr. H.A. Burroughs shot a Parker 12 bore with medium choke weighing but 7 lb 14oz. He shot 4 drachms of Hazard's Electric Powder and 1 1/4 oz. of chilled #7 in the left barrel and #8 in the right.
U.M.C.'s new paper shells were said to be the choice of most to carry their loads.
W&C Scott was the choice for most shooters with a pair of Remingtons and a Moore and a Williams & Powell.

That began to change in the 1880s

In 1883, Dr. W.F. Carver The Evil Spirit of the Plains was matched against Capt. A. H. Bogardus by the Ligowsky Clay Pigeon Co. in a 25-match series. He and Capt. Bogardus shot 100 targets each in 25 different cities, with Carver winning 19 matches, tieing three and losing three.
Bogardus shot a hammerless Scott, 7 lbs 6 oz; Carver a hammerless 12b Greener 7 lbs 12 oz.

A Cashmore hammerless Pigeon gun (I don't have the DOM) marked "3 1/4" CASES"