"To His Coy Mistress" can be compared to what other poem of the same period in regard to the nature of love and relationships?

A poem that springs immediately to mind, of roughly the same period, is "To the Virgins, To Make Much of Time" by Robert Herrick.  The message of both poems is the same -- there is not very much time in this world, and we are only young for a short period of that time; and for this reason, the poets are saying, the mistress should yield to the advances of the lover.  While the poems are not exactly contemporary (Herrick's was published in 1648, while Marvell's was 1681,) and the meter and styles are somewhat different from each other, by the time Marvell was publishing his poems (in the case of this one, posthumously) his kind of lyric poety was considered somewhat old fashioned (Hollander and Kermode 641.)  So it's entirely possible that Marvell's poem was written closer to Herrick's date than the publication date reflects (probably the 1650s, Ibid), and the theme of "carpe diem" (seize the day) is therefore justifiably similar.

As to the content of the poems, they are very similar indeed.  The message is that time is fleeting (or, as Marvell would say it in the subjunctive, meaning the opposite "Had we world enough and time" (1)) so the female object of the poem should yield to her lover's romantic overtures.  The theme is very old, originated probably by Asclepiades (3rd Century B.C.E., Greek, 648), reminding young women that they will not be young and beautiful forever, and there is no love-making in the afterlife.  Compare these two passages:

That long-preseved virginity,
And your quaint honour turn to dust,
And into ashes all my lust:
The grave's a fine and private place,
But none, I think, do there embrace.  (Marvell, 28-32)

Then be not coy, but use your time,
And while ye may, go marry:
For having lost but once your prime,
You may forever tarry.  (Herrick, 13-16)

This theme of wasting time (or, as Marvell masterfully puts it, "Time's winged chariot hurrying near;" (22)) is also central to two other poems of this time.  Ben Jonson's "Come my Celia" (also called "Song: To Celia"), published in 1606, and Edmund Waller's "Go, Lovely Rose" (1645) say essentially the same thing: time is rushing on, and we must seize the moment and our love.  The poems are different in their intensity, and also in the amount of allusions and imagery they contain.  Marvell's is the most dense and erudite, arguably, with the most vivid imagery.  Jonson's is much more a song than a poem, with a more directly Christian overtone than the others

Come, my Celia, let us prove,
While we may, the sports of love;
Time will not be ours forever:
He, at length, our good will sever. 
Spend not then his gifts in vain: (1-5)

 and Waller's is perhaps the most poignant,

Small is the worth
Of beauty from the light retired:
Bid her come forth,
Suffer herself to be desired,
And not blush so to be admired. (11-15)

 while Herrick's, in flippant tetrameter, is perhaps the most playful.  To say essentially the same thing in different ways is the prerogative of poets, and each of these Renaissance poets does it admirably. 

Source: The Literature of Renaissance England.  Hollander, John, and Frank Kermode, eds.  New York: Oxford University Press, 1973.