We present an analysis of broad emission lines observed in moderate-luminosity active galactic nuclei (AGNs), typical of those found in X-ray surveys of deep fields, with the aim to test the validity of single-epoch virial black hole mass estimates. We have acquired near-infrared (NIR) spectra of AGNs up to z ~ 1.8 in the COSMOS and Extended Chandra Deep Field-South Survey, with the Fiber Multi-Object Spectrograph (FMOS) mounted on the Subaru Telescope. These low-resolution NIR spectra provide a significant detection of the broad Halpha line that has been shown to be a reliable probe of black hole mass at low redshift. Our sample has existing optical spectroscopy which provides a detection of MgII, a broad emission line typically used for black hole mass estimation at z > 1. We carry out a spectral-line fitting procedure using both Halpha and MgII to determine the virial velocity of gas in the broad line region, the monochromatic continuum luminosity at 3000 A, and the total Halpha line luminosity. With a sample of 43 AGNs spanning a range of two decades in luminosity (i.e., L ~ 10^44-46 ergs/s), we find a tight correlation between the continuum and line luminosity with a distribution characterized by = 1.52 and a dispersion sigma = 0.16. There is also a close one-to-one relationship between the FWHM of Halpha and of MgII up to 10000 km/s with a dispersion of 0.14 in the distribution of the logarithm of their ratios. Both of these then lead to there being very good agreement between Halpha- and MgII-based masses over a wide range in black hole mass (i.e., M_BH ~ 10^7-9 M_sun). We do find a small offset in MgII-based masses, relative to those based on Halpha, of +0.17 dex and a dispersion sigma = 0.32. In general, these results demonstrate that local scaling relations, using MgII or Halpha, are applicable for AGN at moderate luminosities and up to z ~ 2. ; Comment: Submitted to ApJ, 9 pages, 7 figures