Sometimes it's good to have a short refrain for the Prayers of the People / Intercessions.Here are a few ideas.
*TiS 741 / AoV1-017 / ATE 282 / LBW368 / ELW407 / GA431 / SFFS 2200 / G(II)410 / GC586 / GC(II)566 / Taize / W&R484 / Srce519 / URW390 O Lord hear my prayer (Berthier) A simple and very well known Taize chant. Works well during intercessions. Good for kids.
URW311 I love you Lord you hear my cry (Watts) A simple song with two verses, or you could use it as a Psalm refrain with the text read by a leader. It would be pretty amazing if you can sing it in 4 parts, I reckon. The 2nd verse could be quite appropriate on its own during intercessions.
Online resource Come in your fullness / Lord hear our prayer (Langmead) A good and quite simple response. Sheet music and sound sample.
GC(II)554 / G(3)664 Lord hear our prayer (Lawton) A very simple prayer response. Good if you'd like an alternative to the Taize "O Lord hear my prayer". Could be used as a response during intercessory prayers. Lead sheet. Sound sample (is that an accordion?).
Worldmaking.net / CP086 / SP&P More Than We Can Ask A great chant for use during intercessions. Very simple and genuine. Sound sample and lyrics.
*AoV2-070 / ATW 496 / MV090 / StJ / G(3)719 Don't be afraid (Bell) Excellent. I love this song of reassurance. "Don't be afraid, my love is stronger. My love is stronger than your fear". This song can be used as a response to intercessions. Good for kids.
GC(II)753 / G(3)860 Watch O Lord (St. Augustine / Haugen) Lovely gentle prayers of intercession for an evening service. A bit schmaltzy, but worth it. The verses have a cantor and response.
Iona (LFB) / Lau930 Listen Lord (Iona / Bell) Beautiful chant-like chorus, can be used on its own or as a response, or used with the verses. Good to use for the intercessions.
MV096 And when you call for me (Bauman / Good) This simple chant "And when you call for me I have already answered... I am already there" might work nicely during the prayers of intercession. Tune is not immediately easy, so teach your congregation first. Good for kids.
AoV2-137 / Iona (SBL) / CH262 For the world and all its people (Somos Pueblo) This is a beautiful, haunting song. It will need to be taught, but once your congregation gets it, I'm sure they'll love it. Particularly good to use during intercessions.
Kyries are also very useful as prayer responses.