Try running in the water and not over land. I don't know if it was just luck or an actual game mechanic, but I seemed to get them more often that way. I know the cloudburst in cloudy weather is only in a very specific area, so it wouldn't surprise me if the same was true for them.
Also, get a collector's catalog from the chocobo races or find a mob with item finder who can fit into your party.
To increase odds of getting item: If you've unlocked Academia 4XX AF, get the Silver Chocobo by throwing Mog (with the Improved Moogle Throw Fragment Skill) at the thing that is projecting the Cocoon holoimage at the Academy Headquarters. Level him with Potent materials (I say this because they are the best choice to make him a race chocobo) until he learns Item Scavenger II. Win all Potent Essence battles with him in the party.
Depending on whether you're on GameFAQs or GameSpot, I am BMSirius and Baron_Von_Stone. We're the same person. Just saying it now to prevent confusion...