Unless another popular Ohioan can be found you probably get President Tilden in 1876. Hayes carried his home state by a single percentage point, and just about any other Republican would probably have lost it.
Hayes's strength is not only that he comes from the key state of Ohio, but that he had sufficient reform credentials to get the support of Carl Schurz and other Liberal supporters of 1872.
However, are we sure that without Hayes, the Democrats would nominate Tilden? Suppose William Allen was re-elected governor of Ohio in 1875--in OTL he was narrowly defeated by Hayes:
William Allen : 292,273
Rutherford B. Hayes : 297,817)
https://en.wikipedia.org/wiki/Ohio_gubernatorial_elections
See a DBWI I once wrote about this:
***
> Other candidates for most undeservedly obscure figures in AH?
Governor William Allen of Ohio, who narrowly won re-election against ex-
governor Rutherford Hayes in 1875. That may seem trivial, but if Hayes had
won, he might well have been the Republican candidate for president in 1876,
and might even have won (he was probably the only Republican candidate who
could have carried Ohio that year).
But that was not the only significance of Governor Allen's victory. Allen
was a leading supporter of the soft-money wing of the Democratic party. His
victory was a smashing rebuke to the hard-money forces led by Governor Tilden
of New York. (Indeed, it is said that Tildenites were secretly financing
General Hayes' campaign.) Moreover, the momentum it generated led to another
soft-money Democratic victory in Pennsylvania a month later. After that,
Tilden was finished. The Democrats in 1876 nominated a soft-money man,
Senator Thomas Hendricks of Indiana, who defeated the Republican candidate
James Blaine. Although President Hendricks was not able to get the
Resumption Act repealed, he did the next best thing by remonetizing silver
and reversing the "crime of 1873." Thus, the nation was spared what might
otherwise have been decades of deflation.
So without William Allen we might have had a choice between two hard-money
men--Hayes and Tilden--in 1876. Ugh.
https://groups.google.com/d/msg/soc.history.what-if/53YbbB7B9Sc/Ja6nP3GoNy0J