There we will sit upon the rocks
And see the shepherds feed their flocks,
By shallow rivers, to whose falls
Melodious birds sing madrigals
There is mild alliteration in this stanza, but it is a rather effective poetic device. Some of the alliterations occur at the beginning of words, while the sibilant alliterations (sibilants are "s's", "sh's", soft "c's", "x's", and sometimes "z's") also occur in the middle of words. Let's examine both kinds.
The word-beginning alliteration in line one "we will" is probably not significant; they are common words which often occur together. Of more import is the use of the imperative form of the verb "will" rather than "shall" (the rule, by no means fixed in Marlowe's time, is that the first-person pronouns "I" and "we" take "shall", unless it is the imperative mood -- then it takes "will". The second- and third-person pronouns are the exact reverse). Did Marlowe mean this auxiliary verb simply for alliteration, or was the imperative mood intended? If the imperative was intended, then this sounds less like a love poem than a exhortation to his beloved ("we WILL sit upon the rocks" -- as if she were denying it). But if it was meant as alliteration, it was probably merely to give lightness and flippancy to the line; a goal which is realized admirably. Also, in this line the first sibilants appear ("sit" and "rocks", although "sit" is weak).
"And see the shepherds feed their flocks" continues the flurry of sibilants (are now up to six in only two short lines). There is definitely a pattern developing here -- but what is the meaning of it? The answer lies in the next line. But before we discuss that the "feed" and "flocks" alliteration is also of minor significance. The pastoral poem in English, of which this is an example, often used the "f" alliteration (Sir Philip Sidney's The Countess of Pembroke's Arcadia is an example in the earlier part of the sixteenth century), presumably because shepherds, those staples of pastoral poetry, tend "flocks", making the "f" alliteration inevitable. Marlowe knew of these conventions, and either included it out of homage, necessity, or even as parody. No one knows for sure, but the poem can be read any of these ways.
"By shallow rivers, to whose falls" -- the count of sibilants is now up to ten! This line as the answer to the question of "why" there is alliteration (although, thankfully, it is not excessive!) in this stanza. The location of the rocks on which the lovers will sit is not the "craggy mountains" of the first stanza, but rocks by "shallow rivers"! The sibilant alliteration is meant as a onomatopoeia. The sound of the "s's" is supposed to mimic the sound of the water, especially if the reader is imagining a shallow river full of little water falls, as depicted by the poets. The "f" alliteration is repeated in "falls", but it is probably of no matter.
"Melodious birds sing madrigals" -- the sibilants are now at fourteen. This new alliteration of "m" is not signficiant, except possibly to bring in the auditory idea of humming (like the birds? this is a bit weak). The "m's" were chosen probably for the lenth of the words they start with "melodious" and "madrigals", so that they fit neatly into the line,and also for the charming nature of their meanings. Madrigals are a kind of song sung in harmony, and the idea of birds harmonizing with each other is meant as an analogy for harmonious love between the lovers.