We present new results on [C $II$]158 $\mu$m emission from four galaxies in the reionization epoch. These galaxies were previously confirmed to be at redshifts between 6.6 and 7.15 from the presence of the Ly$\alpha$ emission line in their spectra. The Ly$\alpha$ emission line is redshifted by 100–200 km s$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ compared to the systemic redshift given by the [C $II$] line. These velocity offsets are smaller than what is observed in $z$ ~ 3 Lyman break galaxies (LBGs) with similar UV luminosities and emission line properties. Smaller velocity shifts reduce the visibility of Ly$\alpha$ and hence somewhat alleviate the need for a very neutral intergalactic medium at $z$ ~ 7 to explain the drop in the fraction of Ly$\alpha$ emitters observed at this epoch. The galaxies show [C $II$] emission with $L$[C $II$] = 0.6 - 1.6 $\times$ 10$8L\odot$: these luminosities place them consistently below the star formation rate (SFR)–$L$[C $II$] relation observed for low-redshift star-forming and metal-poor galaxies and also below $z$ = 5.5 LBGs with similar SFRs. We argue that previous undetections of [C $II$] in $z$ ~ 7 galaxies with similar or smaller SFRs are due to selection effects: previous targets were mostly strong Ly$\alpha$ emitters and therefore probably metal-poor systems, while our galaxies are more representative of the general high-redshift star-forming population.