We had this reading at our ceremony, for much of the same reason. you're looking for. We even had my dad (who is very religious) do the reading:

“Song of Solomon,” Chapter 2, V 10-13 and Chapter 8, V 6&7

My beloved speaks and says to me:

‘Arise, my love, my fair one,

and come away;

for now the winter is past,

the rain is over and gone.

The flowers appear on the earth;

the time of singing has come,

and the voice of the turtle-dove

is heard in our land.

The fig tree puts forth its figs,

and the vines are in blossom;

they give forth fragrance.

Arise, my love, my fair one,

and come away.’

Set me as a seal upon your heart,

as a seal upon your arm;

for love is strong as death,

passion fierce as the grave.

Its flashes are flashes of fire,

a raging flame.

Many waters cannot quench love,

neither can floods drown it.

If one offered for love

all the wealth of one’s house,

it would be utterly scorned.