We present a large sample of H- and K-band spectra of 32 optically line luminous central cluster galaxies. We find significant rovibrational H_2 emission in 23 of these galaxies as well as H recombination and/or [FeII] emission in another 5. This represents a fourfold increase in the number of molecular line detections known. A number of the detections are of extended emission (5-20 kpc). In several objects we find significant [SiVI] emission that appears to correlate with the strength of high ionization lines in the optical (e.g. [OIII]). This comprehensive sample builds on previous work and confirms that warm (1000-2500K) molecular hydrogen is present wherever there is ionized material in the cores of cooling flows and in most cases it also coincides with CO molecular line emission.