  We present deep optical imaging and photometry of four objects classified as
"Almost-Dark" galaxies in the ALFALFA survey because of their gas-rich nature
and extremely faint or missing optical emission in existing catalogs. They have
HI masses of $10^7$-$10^9$ $M_{\odot}$ and distances of $\sim$9-100 Mpc.
Observations with the WIYN 3.5m telescope and One Degree Imager reveal faint
stellar components with central surface brightnesses of $\sim$24-25
$\mathrm{mag}\,\mathrm{arcsec}^{-2}$ in the g-band. We also present the results
of HI synthesis observations with the Westerbork Synthesis Radio Telescope.
These Almost-Dark galaxies have been identified as possible tidal dwarf
galaxies (TDGs) based on their proximity to one or more massive galaxies. We
demonstrate that AGC 229398 and AGC 333576 likely have the low dark matter
content and large effective radii representative of TDGs. They are located much
farther from their progenitors than previously studied TDGs, suggesting they
are older and more evolved. AGC 219369 is likely dark matter dominated, while
AGC 123216 has a dark matter content that is unusually high for a TDG, but low
for a normal dwarf galaxy. We consider possible mechanisms for the formation of
the TDG candidates such as a traditional major merger scenario and gas ejection
from a high velocity fly-by. Blind HI surveys like ALFALFA enable the detection
of gas-rich, optically faint TDGs that can be overlooked in other surveys,
thereby providing a more complete census of the low-mass galaxy population and
an opportunity to study TDGs at a more advanced stage of their life cycle.
