Psalm 45 is the closest we get to a love song in the Psalter. The poem is by the sons of Korah addressed first to the king, probably Solomon, then in a second voice to the bride. (v. 10) Hebrews 1 quotes verse 6 (and a clutch of other psalms) in relation to Jesus.
Being more in the style of an official paean, it may not reach the poetical and romantic heights of the Song of Solomon. However, some sweet lines freshen the formal reminders of the importance of truth and loyalty:
All your garments are fragrant with myrrh, aloes and cassia, and the music of strings from the ivory palaces makes you glad (v. 8)
Everett in The Emergent Psalter picks up these nice lines for his antiphon.
Others — such as the very simple home-grown refrain illustrated, and the fragment of Martin Luther’s Ein Feste Burg in Psalms for All Seasons — focus on divine goodness. The alternate refrain to that setting 45B is by John Bell. Creative as always, he stretches his interpretation widely and borrows and bends a phrase from the Song of Solomon 8:6 in his refrain:
Take O take me as I am; summon out what I shall be; set your seal upon my heart and live in me.
A curious find tucked away in CPDL is a transcription by Joachim Kelecom of a Corsican communion chant for three voices, Beata viscera. It is said to be a verse of Psalm 45 but the text is Marian. For authenticity you might need agile and perhaps Corsican voices for the many ornamentations and effects.