  We apply the Lunin--Maldacena construction of gravity duals to beta-deformed
gauge theories to a class of Type IIB backgrounds with U(1)^3 global symmetry,
which include the multicenter D3-brane backgrounds dual to the Coulomb branch
of N=4 super Yang-Mills and the rotating D3-brane backgrounds dual to the
theory at finite temperature and chemical potential. After a general
discussion, we present the full form of the deformed metrics for three special
cases, which can be used for the study of various aspects of the
marginally-deformed gauge theories. We also construct the Penrose limits of the
solutions dual to the Coulomb branch along a certain set of geodesics and, for
the resulting PP--wave metrics, we examine the effect of beta-deformations on
the giant graviton states. We find that giant gravitons exist only up to a
critical value of the sigma-deformation parameter, are not degenerate in energy
with the point graviton, and remain perturbatively stable. Finally, we probe
the sigma-deformed multicenter solutions by examining the static heavy-quark
potential by means of Wilson loops. We find situations that give rise to
complete screening as well as linear confinement, with the latter arising is an
intriguing way reminiscent of phase transitions in statistical systems.
