$CO_2$ is well known greenhouse gas which is the major source of global warming. Reducing $CO_2$ emission in combustion process can be achieved by increasing combustion efficiency, oxygen enriched combustion and recirculation of the emitted $CO_2$ gas. Stability of non-premixed flame in oxygen enriched environment will be affected by the amount of oxygen, kind of diluents and fuel exit velocity. The effects of these parameters on flame liftoff and blowout are studied experimentally oxidizer coflowing burner. Experiments were divided into three cases according as where $CO_2$gas was supplied. - 1) to coflowing air, 2) to fuel with 0$_2$-$N_2$ coflow, 3) to coflowing oxygen. Flame in air coflowing case was lifted in turbulent region. Flame lift and blowout in laminar region with the increase in $CO_2$ volume fraction in $CO_2$-Air mixture makes flame lift and blowout in laminar region. Increase in oxygen volume fraction makes flame stable-i.e. flame liftoff and blowout occur at higher fuel flowrates. Liftoff height was non-linear function of nozzle exit velocity and affected by the $O_2$ volume fraction. It was found that the flame in $O_2$-$N_2$ coflow case was more stable than $O_2$-$CO_2$ case, Liftoff heights vs (nozzle exit velocity/laminar burning velocity)$^{3.8}$ has a good correlation in $O_2$-$CO_2$ oxidizer case.