The question is actually more difficult than it seems since there are so many factors one needs to consider in order to make a final determination. One should understand that the tragedy arose because of a number of unfortunate issues and events which all added to the drama.
In the first place, if there had been no feud between the two families, the tragedy might never have occurred, for it was the primary cause for all the succeeding events. It was because of this that our two star-crossed lovers had to meet in secret, Tybalt killed Mercutio, Romeo retaliated by killing Tybalt and Romeo was banished. Furthermore, the feud also led to friar Laurence marrying the two doomed lovers in secret in the hope that their marriage would lead to a resolution of the conflict between the two families.
It is, therefore, clear that all those involved in these circumstances were in some way or another complicit in the eventual suicide of the two infatuated youngsters, including themselves. They were much too impulsive and naive and quickly accepted whatever guidance they were given, especially by friar Laurence. The question, however, remains: who, out of all those involved, was most responsible?
Clearly, the one whose actions led directly to their demise should be seen as most complicit in this regard, and it seems as if friar Laurence is the most guilty. Firstly, he is the one who so easily acquiesced to Romeo's request for a marriage. Instead of advising against such an impulsive step, the friar naively assumed that it would act as an incentive for the warring families to realize the folly of their fight since love conquers all. He tells Romeo in Act 2, scene 3:
But come, young waverer, come, go with me,In one respect I'll thy assistant be;For this alliance may so happy prove,To turn your households' rancour to pure love.
His meddling, though, created more problems.
Added to that, the friar's support for their illicit affair encouraged the two lovers and was most probably the reason why Romeo refused to engage Tybalt in a swordfight leading to Mercutio's fiery intervention and subsequent death. This, in turn, led to avenging his best friend's death and he killed Tybalt in a subsequent duel. He was then banished at the risk of death.
Furthermore, it was the friar who told Juliet to drink a sleeping potion to fake her own death so that she could escape having to marry Paris. It would have been immoral for her to do so since she was already married to Romeo, and she obviously did not love Paris. The friar tells her in Act 4, scene 1:
Take thou this vial, being then in bed,And this distilled liquor drink thou off;When presently through all thy veins shall runA cold and drowsy humour, for no pulseShall keep his native progress, but surcease:No warmth, no breath, shall testify thou livest;The roses in thy lips and cheeks shall fadeTo paly ashes, thy eyes' windows fall,Like death, when he shuts up the day of life;Each part, deprived of supple government,Shall, stiff and stark and cold, appear like death:And in this borrow'd likeness of shrunk deathThou shalt continue two and forty hours,And then awake as from a pleasant sleep.
This act brought about greater complications since Romeo did not receive the friar's urgent message about Juliet's true condition and he, believing that she was indeed dead, killed himself; she later did the same on discovering her love's corpse next to her.
The friar's actions truly epitomise the expression: 'The road to hell is paved with good intentions.' It was his desire to do good that directly led to the unfortunate deaths of both our inexperienced and impulsive lovers.