You can read the Platonic epigrams online in English at the Perseus Project, and ten of them in a different English translation at Wikisource. Percy Bysshe Shelley translated a couple of them.
The Star Epigrams
Perhaps the most famous epigrams attributed to Plato are the Star epigrams. The major reason for thinking them inauthentic, as with many of the epigrams, is that they have features suggestive of much later poetry. In this epigrams we have someone addressed as a star, perhaps because his name or nickname was Aster:
You gaze at the stars, my Star; would that I were Heaven that I might look at you with many eyes!
Even as you shone once the Star of Morning among the living, so in death you shine now the Star of Evening among the dead.
Or to take the latter in Shelley's slightly looser but excellent translation of the latter:
Thou wert the morning star among the living,
Ere thy fair light had fled;—
Now, having died, thou art as Hesperus, giving
New splendour to the dead.
It's common for Greek epigrams to come in pairs. In the first epigram, the beloved, called a star, looks at the stars, so the lover wishes he were the sky (ouranos) so that he could look back at the beloved with many eyes (the many eyes being the stars). I think I would paraphrase it as:
Stars you watch, my star;
would I were the sky
looking back at you,
each star a shining eye.
It reminds one a bit of the argument for the importance of dialogue in Alcibiades Major, in which Socrates argues that self-knowledge requires seeing oneself in the eyes of another, but self-knowledge is not yet in view here. Rather, Alcibiades Major is taking the kind of idea that this epigram draws on, and putting it to new use.
The second Star epigram plays on a common Greek idea that the dead became stars, and on the association of life with morning and death with evening combined with the fact that the morning star and the evening star are the same, and both associated with love.
The Apple Epigrams
My favorite Platonic epigram is among those that have the best claim to being authentic:
I throw the apple at you, and if you are willing to love (phileis) me, take it and share your girlhood (partheneis) with me; but if your thoughts are what I pray they are not, even then take it, and considered how short-lived (oligochronios) is beauty.
The apple, of course, was a symbol of love to the ancient Greeks; 'to throw an apple at someone' became synonymous with declaring one's love for them. This is good solid work in any language; combining an expression of love with a "But if you do not love me, at least remember that your moments for really living are few" is a standard love poetry trope, and here it is concisely and vigorously expressed.
There is another apple poem, this one addressed to Xanthippe -- one would assume in the voice of Socrates:
I am an apple; one who loves you throws me at you. Say yes, Xanthippe; we fade, both you and I.
Here we have a greater emphasis on conciseness, although the same theme.
The Dion Epigram
According to Diogenes Laertius, Plato wrote an epitaph for Dion's tomb in Syracuse:
The Fates decreed tears to Hecuba and the women of Troy right from their birth; but for you, Dion, the gods spilled your widespread hopes upon the ground after you had triumphed in the doing of noble deeds (kalon epinikion ergon). And so in your spacious homeland you lie honored by your fellow citizens, O Dion, you who made my heart mad with love.
Of all the epigrams, this is the one most likely to be authentic if any is. Hecuba and the Trojan women, of course, is a famous tale from the aftermath of the Trojan war; Euripides has a particularly brutal telling of it. Thus the tale is associated with the loss of a city, and a fit opening for the loss of Dion and the vision of the city lost with his death. But a contrast is made between the lead-up to each disaster, since Dion's disaster occurs in the aftermath of noble works. Perhaps more interesting is the linking of thymos and eros in the last line: 'who drove mad my thymos from eros, Dion'. Thymos is that part of the soul that rises to challenges, loves victory, and seeks out difficulties to overcome. It's difficult not to think of Phaedrus or Symposium in reading of eros in this context, as well as the calmer emphasis of the Platonic Letters on the fundamental importance of friendship and companionship for the accomplishing of great things.
There are several other epigrams, often addressing or mentioning people we recognize from elsewhere: Phaedrus, Agathon, Sappho, the sculptor Praxiteles, and Aristophanes. The most famous of these is that which speaks of Sappho, since it gives us a famous description of her as the Tenth Muse:
Some say there are nine Muses. How thoughtless! Look at Sappho of Lesbos; she makes a tenth.
There are also two epigrams attributed to Plato on the deportation of the Eretrians during the Persian Wars after the Siege of Eretria, two concerning women about whom we know nothing else (Archeanassa and Lais), and some more generic pieces.
Quotations are from John M. Cooper's revision of J. M. Edmonds's translation, in Plato, Complete Works, Cooper & Hutchinson, eds., pp. 1742-1745.