We present near-infrared spectra obtained to search for Pa \alpha and molecular hydrogen lines in edge-darkened ( FR I-type ) radio galaxies with bright H \alpha emission in the redshift range 0.0535 < z < 0.15 . We find that all three galaxies in our sample ( PKS 0745-191 , PKS 1346+26 , & PKS2322-12 ) which are associated with strong cooling flows also have strong Pa \alpha and H _ { 2 } 1–0 S ( 1 ) through S ( 5 ) emission , while other radio galaxies do not . Together with earlier observations this confirms claims that cooling flow galaxies are copious emitters of molecular hydrogen with large H _ { 2 } 1–0 S ( 3 ) /Pa \alpha ratios in the range 0.5 to 2 . The emission is centrally concentrated within the inner few kiloparsec and could come from warm ( T \simeq 1000-1500 K ) molecular material which is being deposited by the cooling flow . We speculate that the H _ { 2 } emission could be related to the interaction between the jets and this molecular gas .