http://www.h-net.org/~business/bhcweb/publications/BEHprint/v022n2/p0036-p0066.pdf#search=%22oil%20r unning%20out%201890%22

This may be the first 3:

The fountainhead of the modern American conservation movement, George Perkins Marsh...estalished major foci and themes, including alarm at the exhaustion of natural resources...The first critics to direct Marsh's concepts towards petroleum and say that America would run out
of oil were Pennsylvania geologists.  From 1883 onward, J. Peter Lesley and John F. Carll warned that producers were depleting Pennsylvania oil fields so rapidly that the reserves would exhaust in a generation, and there was "no reasonable ground" to expect large new discoveries.

Thus, in 1908, George Otis Smith...assigned David T. Day...to report on petroleum reserves for the National Conservation Commission...Day offered an alarming view of American petroleum reserves...he concluded that the United States had between 10 and 24.5 billion barrels of oil
left, inclining to 15 billion barrels as the likeliest fiture...he argued that if production continued to increase as it had in the past, oilmen would exhaust national reserves by 1935...Few conservationist perspectives on petroleum have ever received as much attention and
repetition as Day's.  For the better part of the next two decades, the USGS repeated his alarm in the petroleum section of its annual survey of mineral resources...After the USGS began to spread the alarm, the newly created Bureau of Mines, headed by former USGS employee Joseph Austin Holmes, joined its campaign by warning that the nation was wasting natural gas.

In December 1924, Calvin Coolidge created a Federal Oil Conservation Board (FOCB), appointed the secretaries of the Interior, War, Navy, and Commerce to it, and asked the board to answer such questions as whether there was an "inexhaustible supply" of petroleum in the United States; whether industry and government were "squandering" natural resourcs; and whether petroleum consumption and production could be cut back without disrupting the economy...The preseident's questions reflected two decades of conservationist discourse...They also implied what many critics of the petroleum industry charged outright; that the American petroleum industry had managed a vital natural resource irresponsibly and that it was time for government
to do something about it.

Count the 1970s as #4 and today as #5.