  The diffusion transport coefficients of a binary granular suspension where
one of the components is present in tracer concentration are determined from
the (inelastic) Enskog kinetic equation. The effect of the interstitial gas on
the solid particles is accounted for in the kinetic equation through two
different terms: (i) a viscous drag force proportional to the particle velocity
and (ii) stochastic Langevin-like term defined in terms of the background
temperature. The transport coefficients are obtained as the solutions of a set
of coupled linear integral equations recently derived for binary granular
suspensions with arbitrary concentration [G\'omez Gonz\'alez \emph{et al.},
Phys. Rev. E \textbf{101}, 012904 (2020)]. To achieve analytical expressions
for the diffusion coefficients, the above integral equations are approximately
solved by considering the so-called second Sonine approximation. The
theoretical results for the tracer diffusion coefficient $D_0$ (coefficient
connecting the mass flux with the gradient of density of tracer particles) are
compared with those obtained by numerically solving the Enskog equation by
means of the direct simulation Monte Carlo method. Although the first-Sonine
approximation to $D_0$ yields in general a good agreement with simulation
results, we show that the second-Sonine approximation leads to an improvement
over the first-Sonine correction, especially when the tracer particles are much
lighter than the granular gas. The expressions derived here for the diffusion
coefficients are also used for two different applications. First, the stability
of the homogeneous steady state is discussed. Second, segregation induced by a
thermal gradient is studied. As expected, the results show that the
corresponding phase diagrams for segregation clearly differ from those found in
previous works when the effect of gas phase on grains is neglected.
