  We probe small scalar coupling differences via the coherent interactions
between two nuclear spin singlet states in organic molecules. We show that the
spin-lock induced crossing (SLIC) technique enables the coherent transfer of
singlet order between one spin pair and another. The transfer is mediated by
the difference in cis and trans vicinal J couplings among the spins. By
measuring the transfer rate, we calculate a J coupling difference of $8 \pm 2$
mHz in phenylalanine-glycine-glycine and $2.57 \pm 0.04$ Hz in glutamate. We
also characterize a coherence between two singlet states in glutamate, which
may enable the creation of a long-lived quantum memory.
