  We calculate sensitivity coefficients to $\alpha$-variation for the
fine-structure transitions (1,0) and (2,1) within $^3P_J[2s^2 2p^2]$ multiplet
of the Carbon-like ions C I, N II, O III, Na VI, Mg VII, and Si IX. These
transitions lie in the far infrared region and are in principle observable in
astrophysics for high redshifts z~10. This makes them very promising candidates
for the search for possible $\alpha$-variation on a cosmological timescale. In
such studies one of the most dangerous sources of systematic errors is
associated with isotope shifts. We calculate isotope shifts with the help of
relativistic mass shift operator and show that it may be significant for C I,
but rapidly decreases along the isoelectronic sequence and becomes very small
for Mg VII and Si IX.
