Welcome to the board. For oxygen piping systems I'd recommend using CGA specification G-4.4 "Oxygen Pipeline Systems". Our company uses CGA religiously for stuff like this.
Per G-4.4, para 4.2.5.3, "Materials that are found to be flammable within the very high pressure range [which this falls into] should be subject to oxygen gas velocity limitations as indicated in 4.4. Thickness limitations, where applicable, must be observed." Stainless steel is most definately flammable in this pressure range. In fact, Appendix D of G-4.4 lists austenitic stainless steels as being flammable above 290 psig at any thickness.
Because this is a diverter valve, I'm assuming flow inside the valve is going to turn a corner. That is, I'm assuming the ball has an L shaped internal port where any particles in the flow stream are likely to impinge on the inside of the ball. That leads you to para. 4.4.2, "Impingement velocity curve and metallic material selection for piping and equipment". Figure 1 under this paragraph shows that velocity must be less than roughly 15 ft/second. Flow velocity higher than that can result in impingement incidents igniting the stainless steel.
So to answer your question, stainless steel is not suitable for this type of installation because this is a diverter valve for a relief tree and as such, velocities much higher than 15 ft/s are expected. If you can show velocity won't be higher than 15 ft/s, then per the rules you could use it, but it would be considered very poor practice to do so. As EdStainless has eluded to, plastics in oxygen systems (ie: valve seats) are much more readily ignited and are often found to be ignition points in these systems similar to a blasting cap is the initial ignition point for a large amount of explosive. Once you ignite something like plastic inside a stainless valve or pipe, it's all over - call the fire department! lol
A much better material for the ball and body would be those materials listed in Appendix D which includes exemption pressures for all types of alloys. Those that are exempt up to 3000 psi include:
Brass Alloys (Cast and wrought mill forms)
Copper
Copper-Nickel alloys (Cast and wrought mill forms)
Monel 400
Monel K-500
Nickel 200
Tin Bronzes
That's it. Basically copper and nickel and their alloys are what you need to look for in a valve or pipe material for high pressure oxygen. Red brass pipe for example is very common. Monel is very common for balls in ball valves, and brass alloys for the body. I'd suggest getting a copy of CGA G4.4 here: