This paper presents 1.6-2.2-micron imaging observations of the centers of nine galaxies with high 60-100-micron luminosities. Eight of the nine galaxies contain central 2.2-micron sources that are larger than the point spread function, which typically had a size (FWHM) of 1.0 arcsec. The typical physical size of the 2.2-micron sources is about 0.5 kpc. One of the galaxies (NGC 6240) contains a double source, with the components having a similar separation (about 1.5 arcsec) and position angle to the radio and optical components. The central regions of six out of the nine galaxies have 2.2-micron surface brightnesses that are equal to or greater than the maximum 2.2-micron central surface brightness of a sample of optically selected galaxies. The H-K colors of the central regions of the infrared-luminous galaxies are about 0.5 mag redder than the colors of the central regions of optically selected galaxies. The result that the nuclear 2.2-micron sources in almost all of the galaxies are extended is evidence that most of the 2.2-micron emission is from sources other than active nuclei.