I don't drink coffee, but I imagine that a shu puerh could get rather close to what you seek. You'd have to get something of decent quality though, not the cheap generic shit they sell in supermarkets. And even then, it's an acquired taste for many people.
I'd recommend this: http://www.teavivre.com/loose-leaf-pu-erh/
It's not compressed so you don't have to fiddle around with puerh cakes and it's quite decent if I do say so myself. When I first tried it I was like "goddamn this just tastes like leather and dirt". I wanted to hate it but I actually kinda enjoyed the taste. Now I have like 10 different puerh cakes and bricks in my tea stash. An acquired taste indeed. Anyways, this tea I linked kinda reminded me of coffee at first. Mind you that I don't actually know what coffee tastes like, I only drink tea. Oh and it's gonna be on sale soon. I think 40% off starting tomorrow for a couple of days.
Alternatively, you could try to obtain a 50 year old sheng puerh, but you probably don't have that kind of money. And if you do, you'd just get scammed anyway.
Also, if your tea is bitter you're brewing it wrong. Or it's shit tea. Or both.