Gauge bosons are force carriers. Mesons are composite bosons and have similar characteristics to gauge bosons. Is there any sense in which mesons could act as force carriers?
Yes, mesons may participate in interactions completely analogous to gauge bosons in effective field theories.
One prominent example is the pion in an effective quantum field theory on the level of nucleons, which appears as the force carrier of the force between nucleons in a Yukawa type interaction. In fact, Yukawa first predicted the existence of mesons because they would explain how the nuclear force arises (cf. the history section of the Wikipedia article).