Exclude oxygen by keeping it under nitrogen or argon, and include a metal chelator such as EDTA to inhibit trace metal-catalyzed oxidation.
I've been working with a highly concentrated solution of N-acetylcysteine in water lately, and I haven't noticed any significant oxidation even though the solution is exposed to air and nothing is added to it. I keep it on ice when in use and at -80oC between experiments.
It would be worthwhile to consider what level of oxidation to cystine would be acceptable.