Sam made up this very simple tune a few months back when I wanted to incorporate intercessions into the sung worship of our church. I needed something that would fit in the flow of singing, but not provide too many details of what to pray for. So Sam set a melody to a very simple line: 'Send your blessing Lord' (download attachment on the right).

This little tune can be used in many different ways - and hopefully changed to fit your context. In our context I flowed from another worship song into this chord progression, played it through a few times with the band, and then over the music gently introduced the concept to the congregation. I asked people to raise topics that they wanted to pray for, and had them speak these into roving mics. And the form of our response, our prayer, was to sing this tune.
The words can be changed to suit the topic being prayed for. For example, if a sick member of the congregation is brought up as a topic for prayer, the response may be 'Send your healing, Lord' or for an area of conflict, 'Send your peace, o Lord' and so on.
You could also ask the congregation to pray all out loud at once, in pairs or silently for a particular topic, and then after a moment or so, respond with the tune before introducing the next topic to pray for.
I can also envisage that this idea could be used in a more structured way, in a written prayer or part of a liturgy. In this case, you can plan ahead which phrases to use, and even print the short phrase of music in your service sheet (if you have many music readers in your setting).
The downloadable sheet music also have some simple harmonies to use if you choose to.