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I've never used one, but if you search for belly support band or something like that, amazon has options. This one has good reviews and the answers have opinions from people that say they've used it for running. I haven't noticed any bouncing of my belly when running yet at 17+4.
I got this one and love it. I swear it for every run, but also wear it when I'm walking a lot or at the end of the day when my belly/back start to get sore. Highly, highly recommend. If you have ab tight/soreness this belt is really great for that too.
I've been experiencing side pain since about 28weeks and I'm currently 33. I bought this crazy contraption from Amazon and I wear it when I'm standing for long periods of time or cleaning the house, active things... Also I found that the best investment of my entire pregnancy had been compression socks. If your wife doesn't have them... Get them for her!
Maternity Belt - [link]
Compression Socks [link]
Get a back/belly band like this one!
NEOtech Care Maternity Belt - Pregnancy Support - Waist/Back/Abdomen Band, Belly Brace (Beige, Size M) [link]
Similar size as you and I got this one in a medium: https://www.amazon.com/dp/B01GO2Q2YA/ref=cm_sw_r_cp_api_AhyIybGA2EHC3
That's the style my midwife recommended. The band that goes across the top is optional for extra support but I don't ever use it as it doesn't seem necessary.