We calculate sensitivity coefficients to α variation for the fine-structure transitions (1,0) and (2,1) within P3 J [2 s2 2 p2] multiplet of the carbonlike ions CI, NII, OIII, NaVI, MgVII, and SiIX. 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 α variation in a cosmological time scale. 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 CI but rapidly decreases along the isoelectronic sequence and becomes very small for MgVII and SiIX.