We present Arecibo Legacy Fast ALFA (ALFALFA) and follow-up Giant Metrewave Radio Telescope (GMRT) H i observations of the gas-rich interacting group NGC 3166/9. The sensitive ALFALFA data provide a complete census of H i-bearing systems in the group while the high-resolution GMRT data elucidate their origin, enabling one of the first unbiased physical studies of gas-rich dwarf companions and the subsequent identification of second-generation, tidal dwarf galaxies in a nearby group. The ALFALFA maps reveal an extended H i envelope around the NGC 3166/9 group core, which we mosaic at higher resolution using six GMRT pointings spanning ∼1 deg2. A thorough search of the GMRT data cube reveals eight low-mass objects with gas masses ranging from 4 × 107 to 3 × 108 M⊙ and total dynamical masses up to 1.4 × 109 M⊙. A comparison of the H i fluxes measured from the GMRT data to those measured in the ALFALFA data suggests that a significant fraction (∼60 per cent) of the H i is smoothly distributed on scales greater than 1 arcmin (∼7 kpc at the NGC 3166/9 distance). We compute stellar masses and star formation rates for the eight low-mass GMRT detections, using ancillary Sloan Digital Sky Survey (SDSS) and Galaxy Evolution Explorer (GALEX) data, and use these values to constrain their origin. Most of the detections are likely to be either pre-existing dwarf irregular galaxies or short-lived, tidally formed knots; however, one candidate, AGC 208457, is clearly associated with a tidal tail extending below NGC 3166, exhibits a dynamical to gas mass ratio close to unity and has a stellar content and star formation rate that are broadly consistent with both simulated as well as candidate tidal dwarf galaxies from the literature. Our observations therefore strongly suggest that AGC 208457 is a tidal dwarf galaxy.