We present a novel technique for fitting restframe I-band light curves on a data set of 42 type Ia supernovae (SNe Ia). Using the result of the fit, we construct a Hubble diagram with 26 SNe from the subset at 0.01 < z < 0.1. Adding two SNe at z ~; 0.5 yields results consistent with a flat Lambda-dominated "concordance universe" (OmegaM, Omega Lambda) = (0.25, 0.75). For one of these, SN 2000fr, new near infrared data are presented. The high redshift supernova NIR data are also used to test for systematic effects in the use of SNe Ia as distance estimators. A flat, Lambda = 0, universe where the faintness of supernovae at z ~; 0.5 is due to grey dust homogeneously distributed in the intergalactic medium is disfavoured based on the high-z Hubble diagram using this small data-set. However, the uncertainties are large and no firm conclusion may be drawn. We explore the possibility of setting limits on intergalactic dust based on B - I and B - V colour measurements, and conclude that about 20 well measured SNe are needed to give statistically significant results. We also show that the high redshift restframe I-band data points are better fit by light curve templates that show a prominent second peak, suggesting that they are not intrinsically underluminous.