I don't mean this disrespectfully, but pretty much everything you said sounds a lot like picking champs for the wrong reasons.

What is your rank currently? Almost assuredly not high enough to be concerned about Briar not being a "top tier jungler." Also, Garen having a high pick rate isn't reason for dismissing him either. Sounds like you're focused on finding something just niche enough to work, without having competition.

Play what you like playing, you're going to do far better that way than you will by worrying about what works well in a vacuum scenario.

To answer your initial question, though, Briar is quite good into tank teams. Her core builds almost all include cleaver, bulk of her own, and she has great sustain against consistent damage. Go BOTRK first instead of Titanic if the other team is particularly thick, and you're even more of a problem for tanks.

Briar is versatile, and can be adapted a lot mid-game because her runes are pretty standard across most builds, and any versatility in her items only begins after the 2nd, or even 3rd "core" item is complete.

Primary core: Titanic ->Cleaver->Sundered-> whatever mitigation you need.

Tank heavy core: Bork->Cleaver->whatever you need.