  In this paper we report on the spectral analysis of seven X-ray transients,
which were found to be active during a monitoring campaign of the Galactic
center carried out in 2006 and 2007 using the X-ray telescope aboard the Swift
satellite. This campaign detected new outbursts of five known X-ray transients
and discovered two new systems. Their 2-10 keV peak luminosities range from
1E34 to 6E36 erg/s. Two of the sources discussed in this paper are confirmed
neutron star systems (AX J1745.6-2901 and GRS 1741-2853), while the five others
have an unknown nature. We discuss the characteristics of the observed
outbursts and the duty cycles of the various systems. Several of the detected
transients seem to undergo enhanced X-ray activity with levels intermediate
between quiescence and full outburst. We discuss the possibility that the
subluminous appearance of the eclipsing X-ray burster AX J1745.6-2901 is due to
line-of-sight effects. We detected two type-I X-ray bursts with a duration of
50-60 seconds from AX J1745.6-2901, which we discuss in view of the bursting
behavior of low-luminosity X-ray transients. Assuming that we are dealing with
accreting neutron stars and black holes, we estimate the time-average accretion
rate, Mdot, of the transients, which is an important input parameter for binary
evolution models that attempt to explain the nature of subluminous X-ray
transients. Our estimates lie in the range of 3E-13 Msun/yr < Mdot < 1E-10
Msun/yr, if the systems are neutron star X-ray binaries and between 4E-14
Msun/yr < Mdot < 2E-11 Msun/yr for a scenario where the accreting object is a
black hole. Some of the systems have such low estimated mass-accretion rates
that they possibly pose a challenge for binary evolution models.
