We study the properties of luminous stellar clumps identified in deep, high resolution HST/NIC2 F160W imaging at 1.6um of six z~2 star-forming galaxies with existing near-IR integral field spectroscopy from SINFONI at the VLT. Individual clumps contribute ~0.5%-15% of the galaxy-integrated rest-frame ~5000A emission, with median of about 2%; the total contribution of clump light ranges from 10%-25%. The median intrinsic clump size and stellar mass are ~1kpc and log(Mstar[Msun])~9, in the ranges for clumps identified in rest-UV or line emission in other studies. The clump sizes and masses in the subset of disks are broadly consistent with expectations for clump formation via gravitational instabilities in gas-rich, turbulent disks given the host galaxies global properties. By combining the NIC2 data with ACS/F814W imaging available for one source, and AO-assisted SINFONI Halpha data for another, we infer modest color, M/L, and stellar age variations within each galaxy. In these two objects, sets of clumps identified at different wavelengths do not fully overlap; NIC2-identified clumps tend to be redder/older than ACS- or Halpha-identified clumps without rest-frame optical counterparts. There is evidence for a systematic trend of older ages at smaller galactocentric radii among the clumps, consistent with scenarios where inward migration of clumps transports material towards the central regions. From constraints on a bulge-like component at radii <1-3kpc, none of the five disks in our sample appears to contain a compact massive stellar core, and we do not discern a trend of bulge stellar mass fraction with stellar age of the galaxy. Further observations are necessary to probe the build-up of stellar bulges and the role of clumps in this process.