Yes there have been "specific" UN aircraft.

I remember seeing illustrations of "UN" Saab jet fighters, basic aluminium with blue "UN" lettering in place of the Swedish insignia.

Typically, air units attached to UN "peacekeepers" are in the normal owner-country's colors, with the "UN" in white (in the case of "combat" helicopters).

Humanitarian aid helicopters and aircraft are usually white, with blue "UN".

I do not believe that there is a particular specification, so there is a large variation.