  We study the mass transfer rates and disk stability conditions of
ultracompact X-ray binaries (UCXBs) using empirical time-averaged X-ray
luminosities from Paper I (Cartwright et al. 2013) and compiled information
from the literature. The majority of UCXBs are consistent with evolutionary
tracks for white dwarf donors. Three UCXBs with orbital periods longer than 40
minutes have mass transfer rates above 10^{-10} Msun/year, inconsistent with
white dwarf donor tracks. We show that if helium star donors can retain their
initial high entropy, they can explain the observed mass transfer rates of
these UCXBs. Several UCXBs show persistent luminosities apparently below the
disk instability limit for irradiated He accretion disks. We point out that a
predominantly C and/or O disk (as observed in the optical spectra of several)
lowers the disk instability limit, explaining this disagreement. The orbital
period and low time-averaged mass transfer rate of 2S 0918-549 provide evidence
that the donor star is a low-entropy C/O white dwarf, consistent with optical
spectra. We combine existing information to constrain the masses of the donors
in 4U 1916-053 (0.064+-0.010 Msun) and 4U 1626-67 (<0.036 Msun for a 1.4 Msun
neutron star). We show that 4U 1626-67 is indeed persistent, and not undergoing
a transient outburst, leaving He star models as the best explanation for the
donor.
