In Romeo and Juliet, what example supports the claim that it's a tragic love story?

The tragedy of Romeo and Juliet is foretold in the Prologue to Act I of Shakepeare's play. Indeed, there are three phrases which indicate the tragic nature of the love between the children of mortal foes:

From forth the fatal loins of these two foes 
A pair of star-cross'd lovers take their life; 
Whose misadventur'd piteous overthrows 
Doth, with their death, bury their parents’ strife. 
The fearful passage of their death-mark'd love,...
Is now the two hours' traffic of our stage...(1.1.5-12)

The Prologue states that the "star-cross'd lovers" are marked by fate, while a series of ill-fated events keep them from communicating and being with each other--"misadventur'd piteous overthrows"--and the play elaborates on this situation, the fated love, "their death-mark'd love," in the following two hours.

Two other passages that comment upon the tragic nature of the love of Romeo and Juliet are found in the final act, Act V, as the Prince chides the Capulets and the Montagues:

See what a scourge is laid upon your hate
That Heaven finds means to kill your joys with love....(5.3.303-304)

and he closes the play with these sorrowful remarks,

A glooming peace this morning with it brings. 
The sun for sorrow will not show his head. 
Go hence, to have more talk of these sad things; 
Some shall be pardon'd, and some punished; 
For never was a story of more woe 
Than this of Juliet and her Romeo. (5.3.317-322)

Romeo and Juliet are tragic hero and heroine because they are of noble stature, and through a series of fated events, they are brought to a final downfall because of errors in judgment and inexplicable outside forces that overwhelm the two lovers.

Can you provide evidence that Romeo and Juliet is a tragic love story?

Proof that Romeo and Juliet is a tragic love story include that Romeo killed himself due to a misunderstanding because he believed Juliet was dead, and then she killed herself out of grief.

Divisions of proof are explanations of why your thesis statement is true.  For example, you need to establish elements of tragedy.  One element is that Romeo and Juliet fell in love, but they did not know the family each belonged to.  They fell in love under the naïve premise that all you need is love, and family connections are not important.  Of course, the reality of their situation came crashing down on them.

Is she a Capulet?(125)
O dear account! my life is my foe's debt. (Act 1, Scene 5)

It is tragic because they already fell in love, at first sight, and they do not know what is in store for them.

A second division of proof would have to address the fact that they actually are in love.  You can do this by establishing that it was not just a one night enchantment.  The next day, they were still in love.

Bid her devise some means to come to shrift
This afternoon;
And there she shall at Friar Laurence’ cell
Be shriv'd and married. (Act 2, Scene 4)

Unfortunately, the two young lovers only get one night together, which demonstrates the tragedy: Romeo kills Juliet’s cousin Tybalt in a brawl and is banished.  They are still deeply in love, and have to part.

Finally, the tragedy should be not of their own doing.  To be really tragic, the characters can’t really bring it on themselves through misdeed.  Yes, they were foolish.  Yet they didn’t do anything immoral.  Their deaths were the result of their parents callousness and miscommunications, such as the fact that Friar John was not able to deliver the letting telling Romeo what was going on.