Like Psalm 136, to which the reader should turn for more commentary, this psalm (text here>) is a sort of history lesson or song of praise for the main events in the Torah from creation onwards. Verse 14 promising goodness and justice even repeats a verse of the song that Moses sang after handing over to Joshua.(Deut. 32) The complaint against idolatry (vs. 15 ff) is a repeat of Ps. 115:3-8. The idols of those times are said to be of silver and gold — and nothing much has changed.
Since Psalm 135 is a ‘skip’ and not in the lectionary, three of our four regular modern source books follow suit — skip, and leave us to our own devices. Online, three tunes appear on psalter.org, fine and traditional but all straight 87.87 hymns. None grabs my eye, admittedly through the very inconsistent and unpredictable prism of my itches for this or that idea in music, not least of which is singable, tuneful verses with a good refrain. The classical selections on sites like CPDL and IMLSP offer very interesting historical perspectives but infrequently a song either antiphonal or easy.
This is one of the reasons I often remark on what Isaac Everett is offering in The Emergent Psalter. Sometimes his choice of verse for the refrain may not suit the message of the day but his music is never enervating, always interesting and slightly different. While he leaves the leader to read the verses or to find a tone for the verses, no arduous demand, his refrain for Psalm 135 is characteristically short and tuneful. Free to download from Churchpublishing.org, it has as usual a pleasant chord progression. This one is less syncopated than his normal style and thus easy to sing following a cantor: