1971 - Non-Money Related
Sorry, @Mary-LouA, but I've got one from a year before your 1972 citation, and it's not monetary. This also fits with the OP's 1974 recollections involving speed and its measurement.
Here's an example of someone using "a buck" to mean 100 miles per hour. It's from May or June 1971. The reference is the Arlington High School Yearbook, 1971. Specifically, it's from one of the "self-blurbs" that kids are allowed to put in the margins. There is the girl's name, her address, (I assume) her birth date, and then her note,
NOREEN PAICE, 52 Aberdeen Rd. 10/14/53 Hate matrons [;] happiness is doing a buck ten on Jimmy's CH
"CH" refers to a motorcycle, such as this 1959 Harley Davidson Sportster CH Motorcycle. The best "expansion" of the initialism that I could find was from this Quora post, where Dave Butler gives,
C - Competition. The idea was this bike could be ridden off the road, onto a dirt track, and race. I’d be interested to know [how] that went.
H - High performance.
I’ve heard it said the C means California, and the H means Hot. I’m not a believer.
On the same thread, Marc Whinery says,
CH=kick start
but I'm not as impressed with his supporting arguments.
We can drive our "first earlier known appearance" date (for non-monetary use) back to 5 September 1985 with another baseball reference, @called2voyage. The article is in the San Bernadino Sun (p.34), the article is titled Downing drives Angels past Tigers, and the quote is,
"The stat sheets (which showed him hitting .362 in his last 33 games) are a little misleading," Downing said. "The last two weeks I've only been hitting about .150.
"Actually, when Detroit was in our place (late last month) they kind of cooled me off. The Tigers have kind of cooled me all season, to tell the truth. I'm only hitting about a buck (.100) against them, so it was especially nice to break out of it here."
Here is some data-driven analysis from Google Ngrams.
At this link you'll find a graph showing the usage, as found in Google Books, of the following:
a buck twenty
a buck thirty
a buck forty
a buck fifty
a buck sixty
a buck seventy
a buck eighty
a buck ninety
The first monetary usage from this corpus was from 1922:
The Emerald of Sigma Pi - Volume 8, Issue 4 - Page 248
1922 - Read - More editions
Dear Brother Barr: Enclosed you will find a check for the necessary $1.50, for
which please insure me against losing track of all the latest dope on old Sigma
Pi for another year. Believe me, if a buck fifty ever slid out of jeans as
willingly as this I ...
This isn't the question, though it does show how we can get an answer to this question and see trends. It doesn't catch the usages in 1748 or 1856 noted by the OP, but it's a start.
I must note that literary usage tags behind colloquial usage, most likely more so in 1922 than in the 1990s.
I further narrowed it down with such things as "weighed a buck {-ty}", "went a buck {-ty}" and other similar prepended words. To start, I didn't add the number represented by {-ty}.
The full list of what I tried is below. I think that the most interesting chart, and the one that shows the best usage over time as well as possible starting date, is for "about a buck fifty". Without any rigorous analysis, it looks like the date we're looking for is sometime in the 1970s.
"about"; "weigh", "weighs", "weighed", "weighing", "go", "goes", "went", "going" "do", "does", "did", "doing", "drive", "drives", "drove", "driving", "hit", "hits", "hitting", "bowl", "bowls", "bowled", "bowling", "than", "at least"
P.S. Here is the most interesting usage I found.
Locked Up but Not Locked Down: A Guide to Surviving the American [Prison System]
Ahmariah Jackson, IAtomic Seven, Supreme Understanding - 2011 - Preview
Catching a Buck 50: A “rip” or “Buck 50” is when you get your face slashed by a razor and your cheek opens up like you've got a second mouth. The name “buck fifty” came from the number of stitches usually required for such a wound (150).
The same usage appears in this book, as well as this other one. In the latter, it's used in a poem,
...
And shorties with quick tongues
Who threw disses or spit blades
That left a crescent across your face.
A Buck 50
Taped Up
Shaped up
...
-Patty Dukes
Note the capitalization in "A Buck 50".
This more contemporary (early 21st century) usage is further expounded by user isaiahrobinson on this StraightDope thread:
In West Coast gang culture putting "a buck fifty" across someone's face means cutting them right down across the face with a razor, often from the ear to the corner of the mounth, leaving a scar. The guy who plays Omar Little in [T]he Wire, Michael K. Williams, has a buck fifty scar across his face as shown in this photo.
I don't know if that usage is even remotely relevant but I thought I'd mention it...
The link is dead, but I found this picture of Michael K. Williams on a page about celebrity scars.