You could be
Friar Lawrence from Shakespeare's Romeo and Juliet.
I know much of plants and healing
Friar Lawrence dabbles in herbalism and has much knowledge about the medicinal effects of plants.
I marry many in a place of kneeling
He is also a Catholic friar, and he's the one that tries to marry Romeo and Juliet to unite their families.
One plant I know has two sides of a coin
A balance of nature they are conjoined
After Romeo is banished and Juliet's marriage with Paris seems inevitable, Friar Lawrence instructs Juliet to take a potion made from a plant to fake her death in order to reunite her with Romeo. Hence, the "two sides of a coin" that are "conjoined" are life and death.
One drop too much, there is death
Just enough, you sleep with soft breath
This describes in greater detail what the potion does: it makes you appear dead for a while, but it's really just an extended coma, and you'll be fine when you wake up.
I'm wise friend to a hot-headed boy
That would be Romeo, whose hot-headedness lands him in a lot of trouble throughout the play.
I'm consultant to a shy, pretty girl
This is Juliet, who Romeo has a crush on.
I'm a crafty one, a sneaky man
I can always concoct a good plan
Another reference to the fake death plan, but this plan wasn't so good in the end.
Both wanted to die, I prevented as such
I don't recall either Romeo or Juliet saying they wanted to commit suicide because they were apart. But I can see the Friar acting to prevent that if there were such thoughts.
I sent the boy elsewhere, not much
AFAIK, Romeo was banished by the prince of Verona, not the Friar. Perhaps this is a reference to the letter he sent to Romeo requesting that he come back to Verona?
Gave the girl a way to sleep sound
In a day, I'd see her underground
Yet another reference to the fake death plan. Also, Juliet was buried in a tomb.
As for the title,
Romeo and Juliet has two opposing families, and their "kings" are probably their patriarchs: Capulet and Montague.