In the 1950s there was only a couple that could find coin-sized targets. The majority (even if in the configuration of the standard rod & loop type) would only sound off on larger targets. And were a pain in the b*tt to keep balanced, swing, etc...
I know that there might have been a *few* that could find coin-sized targets, for the following reasons:
a) there was one made during the Korean war for mine-detecting, yet was said to be sensitive enough to detect a quarter to a good 6" or so (can't remember the exact depth). Whether or not it could do that if minerals in soils became present, I don't know. Or how "easily" it could do it, I don't know.
b) Kellyco was started by a man who, upon returning from the Korean conflict, used his skills on a mine detector, to hunt for coins. Perhaps it was the same type as that mine detector in (a) above ? But anyhow, he was said to have found individual coins.
c) Guys hunting CW sites (I don't know what brand/type) were finding individual bullets as far back as the 1950s. So if a machine were sensitive enough to find individual bullets, it stands to reason they'd find coins too.
d) Whites metal detectors came out with their first detector in the very late 1950s (after discontinuing geiger-counters). And that first experimental machine, sent off to a dealer for try-out, was reported to have found various objects at a ghost town, including a coin or two.
e) I have heard of a few early pioneers who started at that time who were already wising up to coin-shoot virgin fairgrounds, parks, etc.... But only as of the very late 1950s. If you're talking the earlier 1950s, I think that was very unknown. Despite Fisher's very early claim to origins (1930s), yet all their early machines were 2-box units. When they eventually made standard detectors, the earlier ones were very dubious on individual coins (and probably not very deep at all).
As for # of inches, if you had the *right* one, and the *right* soil, and the *right operator skill/ears*, I'm betting it was several inches deep, even in the 1950s. But for the most part, the entire USA's parks, schools, beaches, were pretty virgin till the mid 1960s. And some places didn't start seeing detectors till the early or mid 1970s.