A module is called coneat injective if it is injective with respect to all
coneat exact sequences. The class of such modues is enveloping and falls
properly between injectives and pure injectives. Generalizations of coneat
injectivity, like relative coneat injectivity and full invariance of a module
in its coneat injective envelope, are studied. Using properties of such classes
of modules, we characterize certain types of rings like von Neumann regular and
right SF-rings. For instance, R is a right SF-ring if and only if every coneat
injective left R-module is injective.