Or a wildlife rehab.
Or any other who has a healthy rabbit, but imo normal poo would do the job too.
But no, unless cottontails are different to domestic rabbits in that regard, they don't need cecotropes. The does do not leave them lying around for the kits, that would turn the nest into a stinky mess, rabbits main shield against being eaten is to not get noticed.
Baby bunnies might nibble at normal bunny berries though, or get their necessary bacteria from the doe just due to the level of hygiene in a normal nest. I don't know when cottontails begin to nibble food, domestics start at about that age, but afaik cottontails develop faster/start out developed further.
Depending on what age you got that cottontail, most likely it might not need any of that by now, if it's already eating solid food it. It's difficult to keep bacteria from seeding new territory, like baby bunnies, without thorough desinfection anyway.
There might some probiotic products out there that might help if there are issues, but I have no experience with that.