  A systematic approach is developed in order to obtain spherically symmetric
midisuperspace models that accept holonomy modifications in the presence of
matter fields with local degrees of freedom. In particular, starting from the
most general Hamiltonian quadratic in radial derivatives of the variables, we
obtain a family of effective modified constraints that satisfy Dirac's
deformation algebra, which encodes the covariance of general relativity, and
show that (scale-dependent) holonomy corrections can be consistently
implemented. In vacuum, the deformed anomaly-free Hamiltonian is explicitly
written in terms of three free functions and we obtain a weak observable that
can be interpreted as the mass of the model. Finally, as a particular example,
we present a specific covariant polymeric model that remains regular for any
value of the connection components. Some of its physical implications and the
relation with previous studies in the literature are commented.
