We explore both analytically and numerically the properties of doped t-J models on a class of highly frustrated lattices, such as the kagomé and the pyrochlore lattices. Focusing on a particular sign of the hopping integral and antiferromagnetic exchange, we find a generic symmetry-breaking instability toward a twofold-degenerate ground state at a fractional filling below half filling. These states show modulated bond strengths and only break lattice symmetries. They can be seen as a generalization of the well-known valence bond solid states to fractional filling.