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This is the second in a series of papers reporting on a large reverberationmapping (RM) campaign to measure black hole (BH) mass in high accretion rateactive galactic nuclei (AGNs). The goal is to identify super-Eddingtonaccreting massive black holes (SEAMBHs) and to use their unique properties toconstruct a new method for measuring cosmological distances. Based ontheoretical models, the saturated bolometric luminosity of such sources isproportional to the BH mass which can be used to obtain their distance. Here wereport on five new RM measurements and show that in four of the cases we canmeasure the BH mass and three of these sources are SEAMBHs. Together with thethree sources from our earlier work, we now have six new sources of this type.We use a novel method based on a minimal radiation efficiency to identify nineadditional SEAMBHs from earlier RM-based mass measurements. We use a Bayesiananalysis to determine the parameters of the new distance expression, and themethod uncertainties, from the observed properties of the objects in thesample. The ratio of the newly measured distances to the standard cosmologicalones has a mean scatter of 0.14 dex, indicating that SEAMBHs can be use ascosmological distance probes. With their high luminosity, long period ofactivity and large numbers at high redshifts, SEAMBHs have a potential toextend the cosmic distance ladder beyond the range now explored by type Iasupernovae.

Supermassive black holes with high accretion rates in active galactic nuclei: II. the most luminous standard candles in the Universe