  The massive black hole (BH) population in dwarf galaxies ($M_{\rm BH}
\lesssim 10^5~M_\odot$) can provide strong constraints on the origin of BH
seeds. However, traditional optical searches for active galactic nuclei (AGNs)
only reliably detect high-accretion, relatively high-mass BHs in dwarf galaxies
with low amounts of star formation, leaving a large portion of the overall BH
population in dwarf galaxies relatively unexplored. Here, we present a sample
of 81 dwarf galaxies ($M_\star \le 3 \times 10^9~M_\odot$) with detectable [Fe
X]$\lambda$6374 coronal line emission indicative of accretion onto massive BHs,
only two of which were previously identified as optical AGNs. We analyze
optical spectroscopy from the Sloan Digital Sky Survey and find [Fe
X]$\lambda$6374 luminosities in the range $L_{\rm
[Fe\,X]}\approx10^{36}$-$10^{39}$ erg s$^{-1}$, with a median value of $1.6
\times 10^{38}$ erg s$^{-1}$. The [Fe X]$\lambda$6374 luminosities are
generally much too high to be produced by stellar sources, including luminous
Type IIn supernovae (SNe). Moreover, based on known SNe rates, we expect at
most 8 Type IIn SNe in our sample. On the other hand, the [Fe X]$\lambda$6374
luminosities are consistent with accretion onto massive BHs from AGNs or tidal
disruption events (TDEs). We find additional indicators of BH accretion in some
cases using other emission line diagnostics, optical variability, X-ray and
radio emission (or some combination of these). However, many of the galaxies in
our sample only have evidence for a massive BH based on their [Fe
X]$\lambda$6374 luminosities. This work highlights the power of coronal line
emission to find BHs in dwarf galaxies missed by other selection techniques and
to probe the BH population in bluer, lower mass dwarf galaxies.
