  Via correspondence theorems, rational log Gromov--Witten invariants of the
plane can be computed in terms of tropical geometry. For many cases, there
exists a range of algorithms to compute tropically: for instance, there are
(generalized) lattice path counts and floor diagram techniques. So far, the
cases for which there exist algorithms do not extend to non-stationary rational
descendant log Gromov--Witten invariants, i.e.\ those where Psi-conditions do
not have to be matched up with the evaluation of a point. The case of rational
descendant log Gromov--Witten invariants satisfying point conditions (without
Psi-conditions) and one Psi-condition of any power combined with a line plays a
particularly important role, since it shows up in mirror symmetry as
coefficients of the $J$-function. We provide recursive formulas to compute
those numbers via tropical methods. Our method is inspired by the tropical
proof of the WDVV equations. We also extend our study to counts involving two
lines, both paired up with a Psi-condition, appearing with power one.
