Don't know about sniper's bino's. But the U.S.Navy solicited the general public for bino's. They were wanting Zeiss and B&L in either 6X30 or 7X50. I have a pair of binocular's made by Zeiss in 6X30 that have U.S.Navy BU.SHIPS, No. 5245-1942 and the name Mr. Burton E. Henry. If the Navy was asking for binocular's, the Army may have been also.
There are not many photos of US sniper teams with binoculars in WWII. When it came to sniping tactics and equipment the US was probably one of the worst participants in WWII. Most first hand accounts from WWII talk of sniper rifles just handed out (hopefully to someone who was a first class narksman). Some of the receivers had never fired a rifle with a scope attached. Of those lucky enough to actually receive training - most basically got marksmanship training. I have heard next to no accounts of actual US sniping teams operating in europe- shooter and spotter. The Marines probably had it closest to right, but the terrain they were used in was generally wrong.
That being said; I would be willing to bet most US Army snipers that did'nt ditch their 1903A4 for an M1 Garand - probably picked up a pair of German binoculars (6x30).