Is there a metatime required for space-time to change? Space-time is thought to curve and ripple. Is a kind of metatime required in or during
which such events take place?
 A: 
Space-time is thought to curve and ripple. 

Space-time, i.e. the set of all events under consideration (specificly: coincidence events), together with all relations between these events (primarily: by listing who, among all principal identifiable participants, took part any one coincident event), is thought to be not necessarily homogenous and/or isotropic by definition, but (possibly) to consist of distinct regions which (may) differ in terms of suitable measures, such as curvature. 

Is a kind of metatime required in or during which such [differences and distinctions] take place? 

No: at least some measures of (possible) differences are defined intrinsically, appealing only to participants and the coincidence events in which they took part. Some examples are sketched 


*

* here ("Which causal structures are absent from any “nice” patch of Minkowski space?") and 

* here ("Can the vanishing of the Riemann tensor be determined from causal relations?").
A: This is an open problem, the problem of Time in General Relativity and Quantum Gravity (e.g here and here).
The solution would require a (radical) synthesis of General Relativiy, Quantum Field Theory and especially Thermodynamics (the 2nd Law).
Many people, due to the treatment of time parameter in general relativity (general covariance principle), take a stance that (flow of) time is an illusion (sth this author does not agree with).
Another approach is to interpret the time parameter in General (and Special) Relativity as duration time and not as event instant time, this provides a workaround for many cases.
Furthermore work by Prigogine and others has shown that in non-linear systems one can define a unique Liouville-type operator which is not-time symmetric and which can define a (new) unique time-parameter for the dynamic evolution of the system (Prigogine's lecture on the Nobel prize).

The  problem  of  time  in  physics  and  chemistry  is  closely
related  to  the  formulation  of  the  second  law  of
thermodynamics.  Therefore  another  possible  title of  this  lecture
could  have  been: “the macroscopic and microscopic aspects of the
second  law  of  thermodynamics”. It  is  a  remarkable  fact  that
the  second  law  of  thermodynamics  has  played in  the  history  of
science  a  fundamental  role  far  beyond  its  original  scope.
Suffice it to mention Boltzmann’s work on kinetic theory, Planck’s
discovery of quantum theory or Einstein’s theory of spontaneous
emission, which were all  based  on  the  second  law  of
thermodynamics.

