The effects of a moderate concentration of noninteracting dislocations on the axial channeling radiation due to MeV positrons are analytically calculated. The axial potential due to all the six strings surrounding a ⟨110⟩ axial channel in diamond structure is first obtained which is exact up to quartic terms in distance from the central axis of the channel. The particle oscillation period and hence the radiation frequency depends upon the oscillation amplitude. The effects of dislocations are manifested through the modification in the oscillation amplitude of the channeled particle. We have suggested some suitable experiments to test the results.