I am guessing that you mean secular poetry rather than anything biblical? The poems of Browning, Keats etc tend to go on a bit, but there are masses of others that would fit the bill, depending on your tastes - Here are a couple: - "To Anthea Who May Command Him Anything" by Robert Herrick. Bit of a long-winded title, but you could always just call it just "To ? (your loved ones name) and choose any of the verses you like. Have a look at W.H.Auden's "If I Could Tell You" - again, you could pick just a couple of verses.
Though you may well not care, a wedding counts as a public event so you should really seek permission on any modern reading (last 75 years, I think) - Auden, for example, would still be in copyright (it was mentioned on Radio 4 after the popularity of "Stop All the Clocks", used in "4 Weddings & a Funeral"). It may seem petty, but poets don't earn much for their work, so need the royalties. But Shakespeare said plenty on love, and that's long out of copyright!
Shakespeare - sonnet 116 Elizabeth Barrett Browning - How Do I Love Thee 1 Corintians 13 (if you wanted a reading with a religious source but not too bible-thumpy)
Try www.confetti.co.uk
They have loads of ideas for readings suitable for a civil ceremony. We had "Tell me the truth about love" by Auden at ours. I wouldn't worry too much about seeking permission - if you want to be anal about that kind of thing it could be applied to playing modern music at weddings, funerals etc & is seriously unlikely to be persued by the copyright owners.
Once I went to a civil (actually it was humanist) wedding where they had a reading which I think, was by Mark Twain and it was called "The diary of Adam and Eve" which brought tears to my eyes. Also the groom read a poem he had written for the bride. There is also the Shakespeare sonnet which I think starts "let me not to the marriage of minds admit impediment" (my apologies if I quote wrong). I got married in a register office in 1993 myself and we were warned that nothing remotely religious was allowed so for ex. nothing from the Bible. I specifically mentioned the Prophet by Khalil Gibran and the Registrar answered even that would not be allowed because "Prophet" sounded religious to her. I hope they are more flexible for you but I recommend running it by the Registrar first.