Which of the following diatomic species gets stabilised by losing an electron?

Stability based on Bond order. As bond order increases stability increases. 

After loosing an electron,

$$\begin{gathered} O_2^{+}\left(15e^{-}\right)=\mathrm{\sigma }1{\mathrm{s}}^2{\mathrm{\sigma }}^{*}1{\mathrm{s}}^2\mathrm{\sigma }2{\mathrm{s}}^2{\mathrm{\sigma }}^{*}2{\mathrm{s}}^2\mathrm{\sigma }2{{\mathrm{p}}_{\mathrm{z}}}^2\left(\mathrm{\pi }2{{\mathrm{p}}_{\mathrm{x}}}^2\mathrm{\pi }2{{\mathrm{p}}_{\mathrm{y}}}^2\right)\left({{\mathrm{\pi }}_{2{\mathrm{p}}_{\mathrm{x}}}^{*}}^1{{\mathrm{\pi }}_{2{\mathrm{p}}_{\mathrm{y}}}^{*}}^0\right) ; \\ \mathrm{B}.\mathrm{O}=\frac{10-5}{2}=2.5 \\ {\mathrm{N}}_2^{+}\left(13{\mathrm{e}}^{-}\right)=\mathrm{\sigma }1{\mathrm{s}}^2{\mathrm{\sigma }}^{*}1{\mathrm{s}}^2\mathrm{\sigma }2{\mathrm{s}}^2{\mathrm{\sigma }}^{*}2{\mathrm{s}}^2\left(\mathrm{\pi }2{{\mathrm{p}}_{\mathrm{x}}}^2\mathrm{\pi }2{{\mathrm{p}}_{\mathrm{y}}}^2\right)\mathrm{\sigma }2{{\mathrm{p}}_{\mathrm{z}}}^1 ; \mathrm{B}.\mathrm{O}=\frac{9-4}{2}=2.5 \\ {\mathrm{C}}_2^{+}\left(11{\mathrm{e}}^{-}\right)=\mathrm{\sigma }1{\mathrm{s}}^2{\mathrm{\sigma }}^{*}1{\mathrm{s}}^2\mathrm{\sigma }2{\mathrm{s}}^2{\mathrm{\sigma }}^{*}2{\mathrm{s}}^2\left(\mathrm{\pi }2{{\mathrm{p}}_{\mathrm{x}}}^2\mathrm{\pi }2{{\mathrm{p}}_{\mathrm{y}}}^1\right) ; \mathrm{B}.\mathrm{O}=\frac{7-4}{2}=1.5 \\ \mathrm{CN}\left(13{\mathrm{e}}^{-}\right)=\mathrm{\sigma }1{\mathrm{s}}^2{\mathrm{\sigma }}^{*}1{\mathrm{s}}^2\mathrm{\sigma }2{\mathrm{s}}^2{\mathrm{\sigma }}^{*}2{\mathrm{s}}^2\left(\mathrm{\pi }2{{\mathrm{p}}_{\mathrm{x}}}^2\mathrm{\pi }2{{\mathrm{p}}_{\mathrm{y}}}^2\right)\mathrm{\sigma }2{{\mathrm{p}}_{\mathrm{z}}}^1 ; \mathrm{B}.\mathrm{O}=\frac{9-4}{2}=2.5 \end{gathered}$$