Enormous Lyα nebulae, extending over 300−500 kpc around quasars, represent the pinnacle of galaxy and cluster formation. Here we present IRAM Plateau de Bure Interferometer observations of the enormous Lyα nebulae “Slug” (z = 2.282) and “Jackpot” (z = 2.041). Our data reveal bright, synchrotron emission associated with the two radio-loud active galactic nuclei embedded in the targeted nebulae as well as molecular gas, as traced via the CO(3−2) line, in three galaxies (two sources in Slug, and one in Jackpot). All of the CO emission is associated with galaxies detected in their rest-frame UV stellar emission. The total mass in molecular gas of these three galaxies [∼(3 − 5) × 1010 M⊙] is comparable with the total ionized gas mass responsible for the diffuse nebular emission. Our observations place limits on the molecular gas emission in the nebulae: the molecular gas surface density is ΣH2 < 12 − 25 M⊙ pc−2 for the Slug nebula and ΣH2 < 34 − 68 M⊙ pc−2 for the Jackpot nebula. These are consistent with the expected molecular gas surface densities, as predicted via photoionization models of the rest-frame UV line emission in the nebulae, and via Lyα absorption in the Jackpot nebula. Compared to other radio-loud quasars at z > 1 and high-redshift radio-loud galaxies, we do not find any strong trends relating the molecular gas reservoirs, the radio power, and the Lyα luminosities of these systems. The significant step in sensitivity required to achieve a detection of the molecular gas from the nebulae, if present, will require a substantial time investment with JVLA, NOEMA, or ALMA.