Othmar Keel's The Symbolism of the Biblical Worlddemonstrates how ancient Near Eastern iconography illuminates the conceptual world of Psalms. He includes a couple images that might reframe one's understanding of Psalm 137:9.
Psalm 137:9 (NRSV): Happy shall they be who take your little ones and dash them against the rock!
In both images, a young prince sits on the lap of his caretaker and has captives under his feet.
Keel explains that when cities were plundered, the inhabitants of these cities often became subject to princes who were very young. There are a couple biblical examples of very young kings, according to MT: Josiah (2 Kings 22:1; 2 Chron 34:1) and Joash (2 Kings 12:1; cf.11:21; 2 Chron 24:1), "became kings" before they reached the age of 10.
Concerning Psalm 137:9 in light of these images, Keel writes:
Babylon is here personified as a queen. As is shown in Figs. 341 and 342, neighboring peoples were subject to princes who were mere babes in the laps of their wet nurses. These infants manifested the endless continuances of the power of the dynasty. Their death meant the end of despotism. (Keel, 230)
He also discusses Psalm 137:9 in the introduction to this book as an example of (1) the importance of understanding a passage's social and historical context and (2) the importance of studying iconography:
We need to consider, however, whether these "little ones" ought not to be understood just as symbolically as "Mother Babylon." The inhabitants of the oppressor-city or the children of the ruling dynasty concretize the continuation of the unrighteous empire (cf. 341-342). In this vein, one might translate: "Happy is he who puts an end to your self-renewing domination!" Stated thus, the sentence would presumably offend no one, though it too implies brutal consequences. Its brutality, however, is cloaked in the broad mantle of abstract formulation. Such a (often dangerous) dissociation of concrete reality from idea is as foreign to the ancient Near Eastern mode of perception as the dissociation of body and spirit. Ancient Near Eastern perception usually preserves the continuity between the concretum and its related abstract. (Keel, 9)
If Keel's reading is correct, we can at least put to rest the idea that in Psalm 137 the worship of Israel was reduced to a vindictive cry for the horrific murder of their enemies' innocent children.