  Direct-collapse black holes (DCBHs) of mass $\sim 10^4$-$10^5 {M}_\odot$ that
form in HI-cooling halos in the early Universe are promising progenitors of the
$\gtrsim 10^9 {M}_\odot$ supermassive black holes that fuel observed $z \gtrsim
7$ quasars. Efficient accretion of the surrounding gas onto such DCBH seeds may
render them sufficiently bright for detection with the JWST up to $z\approx
20$. Additionally, the very steep and red spectral slope predicted across the
$\approx 1$-5 $\mu$m wavelength range of the JWST/NIRSpec instrument during
their initial growth phase should make them photometrically identifiable up to
very high redshifts. In this work, we present a search for such DCBH candidates
across the 34 arcmin$^{2}$ in the first two spokes of the JWST cycle-1 PEARLS
survey of the north ecliptic pole time-domain field covering eight NIRCam
filters down to a maximum depth of $\sim$ 29 AB mag. We identify two objects
with spectral energy distributions consistent with the Pacucci et al. (2016)
DCBH models. However, we also note that even with data in eight NIRCam filters,
objects of this type remain degenerate with dusty galaxies and obscured active
galactic nuclei over a wide range of redshifts. Follow-up spectroscopy would be
required to pin down the nature of these objects. Based on our sample of DCBH
candidates and assumptions on the typical duration of the DCBH steep-slope
state, we set a conservative upper limit of $\lesssim 5\times 10^{-4}$ comoving
Mpc$^{-3}$ (cMpc$^{-3}$) on the comoving density of host halos capable of
hosting DCBHs with spectral energy distributions similar to the Pacucci et al.
(2016) models at $z\approx 6$-14.
