"Direct collapse black holes" (DCBHs) provide possible seeds for supermassive black holes that exist at z similar to 7. We study Ly alpha radiative transfer through simplified representations of the DCBH scenario. We find that gravitational heating of the collapsing cloud gives rise to a Ly alpha cooling luminosity of up to similar to 10(38)(M-gas/10(6) M-circle dot)(2) erg s(-1). Photoionization by a central source boosts the Ly alpha luminosity to L alpha similar to 10(43)(M-BH/10(6) M-circle dot) erg s(-1), where M-BH denotes the mass of the black hole powering this source. We predict that the width and velocity offsets of the Ly alpha spectral line range from a few tens to few thousands km s(-1), depending sensitively on the evolutionary state of the cloud. We apply our predictions to observations of CR7, a luminous Ly alpha emitter at z similar to 7, which may be associated with a DCBH. If CR7 is powered by a black hole, then its Ly alpha flux requires that M-BH > 10(7) M-circle dot 7, which exceeds the mass of DCBHs when they first form. The observed width of the Ly alpha spectrum favors the presence of only a low column density of hydrogen, log[N-HI/cm(-2)] similar to 19-20. The shape of the Ly alpha spectrum indicates that this gas is outflowing. These requirements imply that if CR7 harbors a DCBH, then the physical conditions that enabled its formation have been mostly erased, which is in agreement with theoretical expectations. These constraints weaken if the observed Ly alpha emission represents the central peak of a more extended halo.