I was surprised to find a literature review about probiotics which suggested they may have significant CNS effects. The tl;dr of the review seems to be: 1) You want doses of at least 109 or 1010 CFU, and 2) You want, in particular, the strains B. longum, B. breve, B. infantis, L. helveticus, L. rhamnosus, L. plantarum, and L. casei.
I then sorted the top 15 results on Amazon for "probiotic" by these desiderata, and found that this one seems to be best.
Some points of uncertainty:
Turns out there's an app (Apple, Android) which compiles evidence from 179 studies on probiotics, ranks them by strength of evidence (study design, etc.) then suggests the most evidence-supported probiotic for a given "indication" (allergies, IBS, etc.). The only available CNS-related indication is "Mood/Affect", though, and the review described in the OP isn't included in the study database, nor were any of the three studies included in that review that I spot-checked. But the two strains it recommends for mood/affect (b. lon... (read more)