  Let $(X, \omega, c_X)$ be a real symplectic 4-manifold with real part $R X$.
Let $L \subset R X$ be a smooth curve such that $[L] = 0 \in H_1 (R X ; Z /
2Z)$. We construct invariants under deformation of the quadruple $(X, \omega,
c_X, L)$ by counting the number of real rational $J$-holomorphic curves which
realize a given homology class $d$, pass through an appropriate number of
points and are tangent to $L$. As an application, we prove a relation between
the count of real rational $J$-holomorphic curves done in math.AG/0303145 and
the count of reducible real rational curves done in math.SG/0502355. Finally,
we show how these techniques also allow to extract an integer valued invariant
from a classical problem of real enumerative geometry, namely about counting
the number of real plane conics tangent to five given generic real conics.
