Is there any way to build Blood DK so that it counters control/copy Priest? Any Tech Cards?

Wanted to try getting diamond at least with blood dk but Control priest was one of the main problems. 

Copy priest decks are so fucking dumb they endless amounts of copying, making it so they just beat any control deck without a hard win condition. 

Are there any counters?

Unfortunately no. Control priest is favored against any control deck that doesn't feature a convincing win con, because they practically have infinite value.

You can theoretically build against control priest, but you'll need to sacrifice some early game for greed. The usual strategy is to have Rivendare, Warrider in your ETC and put Obliterate in your deck so you can rid it yourself.

Put more draw in your deck instead of discover, which will help get that rivendare quickly. Helps with the win con too.

Just be aware that amanthul can poof deathrattles away, so you'd probably want to have more ways to kill your own stuff.

But at the end, theres a good reason why blood DK cant beat control priest and thats because focusing on beating it makes you vulnerable to other decks. Most blood DK players more or less accept that they're going to auto concede against priest.