Following are a number of back-translations as well as a sample translation for translators of Psalm 137:3:

• Chichewa Contempary Chichewa translation, 2002/2016:
  “for the people who captured us into slavery requested us that we sing songs.
  Our persecutors wanted songs of celebration;
  they said, ‘Sing for us one of the songs of Zion!’” (Source: Mawu a Mulungu mu Chichewa Chalero Back Translation)
• Newari:
  “Those who had captured us caused us to sing songs,
  Those who torment us say,
  "Sing a joyful song for us!"
  They say "Sing us a song of Zion!"” (Source: Newari Back Translation)
• Hiligaynon:
  “The ones (who) captured us (excl.) made- us (excl.) -to-sing.
  They commanded us (excl.) to entertain them.
  They said, ‘[You (plur.)] sing us (excl.) a song about Zion!’” (Source: Hiligaynon Back Translation)
• Laarim:
  “for the people who ruled us asked us that, ‘You sing songs.’
  They really wanted our songs of joy,
  and said to us, ‘You sing the songs of Zion!’” (Source: Laarim Back Translation)
• Nyakyusa-Ngonde (back-translation into Swahili):
  “Kwa maana huko ambao walitushika katika utumwa,
  wakataka tuwaimbie nyimbo.
  Ambao walitudhihaki wakataka kwamba tuwafurahishe,
  wakasema, ‘Tuimbieni wimbo mmoja wa katika Sayuni.’” (Source: Nyakyusa Back Translation)
• English:
  “The soldiers who had captured us and taken us to Babylonia told us to sing for them;
  they told us to entertain them/make them happy, saying,
  ‘Sing for us one of the songs that you previously sang in Jerusalem!’” (Source: Translation for Translators)