"Can God make a rock so heavy he can't lift it?"

There are two basic responses.  The most common is that the Bible, and
Christian theology in general, don't have quite such an abstract
concept of omnipotence.  Indeed many current theologians are
uncomfortable with that term.  It's more Greek metaphysics than
Christian theology.  The Bible indicates that God has sufficient power
to get his will done, but doesn't get so abstract.  And God limits
himself in the Incarnation, and in working through the Church.

Those with a more philosophical bent are inclined so say that the
question "can God make a rock so heavy that he can't lift it" is
meaningless.  If you look at what it means, it turns out that the
phrase "so heavy he can't lift it" implicitly assumes that there's a
maximum size rock God can lift.  I.e. it's roughly equivalent to
"there exists a mass M, where God can't lift any rock heavier than M,
and the rock R is heavier than M."  Because we deny the idea that
there is a limit on God's power, we think the phase doesn't actually
describe any possible thing.  So it's no different than asking whether
God can make a square triangle.  Note however that many (maybe most)
Christians will say that God can limit himself.  Thus in some sense
God can make a rock that he can't lift.  I don't think this particular
example makes sense, as I have no idea why he would agree to that
specific limit, but there are certainly things that God has covenanted
that he will not do.

On the metaphorical side, some people say the answer is yes, and in
fact God has done so: he has created the human heart.