Rigid meromorphic cocycles are classes in the first cohomology of SL_2(Z[1/p]) acting on the non-zero rigid meromorphic functions on the Drinfeld p-adic upper half plane. Their values at real quadratic points are conjectured to be analogues of singular moduli for real quadratic fields. In this talk, I will discuss the relation between real quadratic singular moduli and derivatives of p-adic families of modular forms. These results can be fit into an emerging p-adic Kudla program.