  We main goal of this paper is to test whether the NIR peak magnitudes of SNe
Ia could be accurately estimated with only a single observation obtained close
to maximum light, provided the time of B band maximum and the optical stretch
parameter are known. We obtained multi-epoch UBVRI and single-epoch J and H
photometric observations of 16 SNe Ia in the redshift range z=0.037-0.183,
doubling the leverage of the current SN Ia NIR Hubble diagram and the number of
SNe beyond redshift 0.04. This sample was analyzed together with 102 NIR and
458 optical light curves (LCs) of normal SNe Ia from the literature. The
analysis of 45 well-sampled NIR LCs shows that a single template accurately
describes them if its time axis is stretched with the optical stretch
parameter. This allows us to estimate the NIR peak magnitudes even with one
observation obtained within 10 days from B-band maximum. We find that the NIR
Hubble residuals show weak correlation with DM_15 and E(B-V), and for the first
time we report a possible dependence on the J_max-H_max color. The intrinsic
NIR luminosity scatter of SNe Ia is estimated to be around 0.10 mag, which is
smaller than what can be derived for a similarly heterogeneous sample at
optical wavelengths. In conclusion, we find that SNe Ia are at least as good
standard candles in the NIR as in the optical. We showed that it is feasible to
extended the NIR SN Ia Hubble diagram to z=0.2 with very modest sampling of the
NIR LCs, if complemented by well-sampled optical LCs. Our results suggest that
the most efficient way to extend the NIR Hubble diagram to high redshift would
be to obtain a single observation close to the NIR maximum. (abridged)
