Rahul, it will depend (as usual) and I guess, not from any colour dye...Modifications in concentration of proper dye (concentration as low as 0.005% are reported) and application might be recommendable. Solute will depend on whether the cells in culture have to survive after staining or can be/will be fixed prior to staining. For the former think of vital dyes (e. g. methylene blue, trypan blue etc.either hydrous or appropriately buffered hydrous solutions [generally look out for intravital dyes]), for the latter you might use dyes which generally are used for discrete and tender (neuronal) structures: e. g. cresylviolet, methylene blue, toluidine blue, and naturally other variants/types of basic dyes, buffered appropriately or in right solute (e.g. highly diluted Giemsa solution). You for sure will get more detailed answer(s) if you reveal the intended staining step with regard to your general cell culture processing more in detail.
If you don't have Nomarski or phase optics (phase contrast objectives) the only possibility would be to use +/- oblique illumination (condensor aperture is decentered a bit from the optical axis) Result will be a relief-like contrast of structures (like cells in culture) but "real" resolution of the imaging system is lowered. But I guess your Lab(s) will use modern light microscopes...