What are some good bible verses for a christian couple to read together?

1 Corinthians 13.

1 If I speak in the tongues of men and of angels, but have not love, I am only a resounding gong or a clanging cymbal.

2 If I have the gift of prophecy and can fathom all mysteries and all knowledge, and if I have a faith that can move mountains, but have not love, I am nothing.

3 If I give all I possess to the poor and surrender my body to the flames, but have not love, I gain nothing.

4 Love is patient, love is kind. It does not envy, it does not boast, it is not proud.

5 It is not rude, it is not self-seeking, it is not easily angered, it keeps no record of wrongs.

6 Love does not delight in evil but rejoices with the truth.

7 It always protects, always trusts, always hopes, always perseveres.

8 Love never fails. But where there are prophecies, they will cease; where there are tongues, they will be stilled; where there is knowledge, it will pass away.

9 For we know in part and we prophesy in part,

10 but when perfection comes, the imperfect disappears.

11 When I was a child, I talked like a child, I thought like a child, I reasoned like a child. When I became a man, I put childish ways behind me.

12 Now we see but a poor reflection as in a mirror; then we shall see face to face. Now I know in part; then I shall know fully, even as I am fully known.

13 And now these three remain: faith, hope and love. But the greatest of these is love.

Anything in the Bible is a good read.
Specifically:

Song of Solomon is a good book in the Bible to read through together.

Gospel summaries: Romans 1:1-4; 1 Corinthians 15:1-5; 2 Timothy 2:8

Reminder of Christ's work: 1 Peter 3:18; Colossians 1:13-14;

Specifically to do with married couples and/or relationships: Ephesians 5:22-33; 1 Corinthians 7

I include the first two lists since Christ's death and resurrection not only creates Christians, but it also serves as the motivator for Christians to live as they should.

Ephesians chapters 4-6 are devoted mainly to relationships, and focus in part on marriage.
"The Secret of Family Happiness", published by the Watchtower Society covers every aspect of family life and is stuffed with scriptures presented in a most useful way. Go to www.watchtower.org to get your free copy. My wife and i got its predecessor 29 years ago, right after we were married. Its clear exposition of the verses has kept us together and even thriving under the most difficult of problems.

1st--Song of Solomon, the whole thing.
Any of the psalms. They are written in poetry form to be read in groups. Many of the psalms have be set to music.

Leviticus 20:27 is always fun. Exodus 21:7-11 is pleasant too!

There are so many good books with daily reading for couples. Check out Cokesbury or Christian Book Distributors.

Priest 3:13

" Information began to gather and started to pattern in the stargate toward Saturn
between my eye sockets is where I shall build my sky rocket
you don't need any passport, all you need is a thought
the soul becomes hot as coal
the flame blows from the brain holes like volcanos
the brain begins to process as we start this conquest
from this physical bondage, the thought launches
traveling 144 billion light years through the shadows of your imagination
now open your eyes, do you see the flaming arrows aiming at pharoahs of the ancients
as we begin racing like a sparrow through the narrow population
seeking purification, the destination is the holy land
of Bethlehem to eat lamb with Abraham and break bread with the son of man
so slowly hold these hands stretch forth from the skies like a rubber band as we begin to ascend above the land
out of the atmosphere, don't look back we're almost there
just try to prepare and adapt to the air pressure
the search for the mental treasure
pleasure beyond the measures of yards, you can't comprehend God or the distance between stars
picking up quasars inside the radar
going far past any astronaut
moving so fast in this aircraft everything we pass gets hot
when we take off the blast turns glass into rocks
at last my supreme task was to no longer walk on green grass
but to become a beam of gas that travels through an extreme draft
unable to be picked up through cable, out of the reach of all manners of sky examiners, space scanners, giant antennas and high tech cameras
I'm in star mode with the discipline of Dahmo
I broke the U.S. bar code now I'm on God's road
to journey in the realms of the cosmos where only God knows
enter the UFO and give up my work clothes only to glow with a holy robe
explode through the mysterious black holes
deep warp through the outer zone without a phone
to the unknown to sit on my throne alone
the pilot on this galactical plane of knowledge
through culture my sculpture lights up ultra violet
so you could see my brain is symbolic to a palace
therefore I keep my hair stylish, my flesh solid and my teeth polished
next stage, examine my X-ray and take notes for your essay and let the cassette play for as long as a decade as we begin to blaze through the milky ways
repent from our filthy ways, replenish from the guilty days, beyond dreamland, wings span, seven feet
between my eyes is the beak
destination of the flight is to reach the peak
angelical landscapes to take the physical man behind the hidden gates of space, ultimate escapes as we fly at a phenominal rate
as we cruise into magnitude and we break up into a multitude of molecules going through a long hollow tube with a scholars view
wearing the holy white garment, passing sound waves that are supersonic, dodging the comets
star clusters changing my physical structure 'till my lips begin to pucker, kissing Christ at the last supper, grabbing a brass cup of wine, I feel myself get older
sitting on my sofa in a position like yoga 'til my mind passes over the solar system and the super nova
I am the controller, I begin to loosen up my shoulders
forming each joint to the sun's eight points
then I begin to rise like helium, escaping the millenium
I been on Mars, building the holy synogogues for the royal seminars
long before they had the renaissance there existed a Hebrew lodge
a phenomenon from out of the matrix
but the world looks at me with envy and hatred
because I appear to them half naked rising into a spaceship with an arm full of solid gold bracelets "

These are all good ideas, but I think Proverbs is also a good book to read together, as it allows each person to grow and gives you the opportunity to talk about life lived in God's word, not just what the Bible says about couples (although it is healthy to know those). Proverbs is just infinitely useful in everyday life, and going through them together is a great idea.
Ecclesiastes 4:12- "A person standing alone can be attacked and defeated, but two can stand back-to-back and conquer. Three are even better, for a triple-braided cord is not easily broken."
Tripling your strength into God, you, and your significant other is ideal and growing together in God's word is a great way to do it.

My girlfriend and I love reading Revelation together and talking about it. I recommend that one all the way, it can lead to some great discussions and stuff. Now granted, that's not a verse but it can generate hours of fun.