Depending on how long you want the prayer meeting to be, choose one or more of these options. If you do not have a corporate prayer meeting where more than just a few come, any one of these things can be done in 5-10 minutes in a morning worship service.

1. Have a time where ministry leaders come forward (this can be a little difficult if no ministry leaders come to the prayer meetings). You can define ministry leader however you want, but I would make it pretty open. Have them spread out across the front of the room. If you are not sure that everyone in the room knows what ministry each represents, have each leader simply say their ministry. Next invite the people in the room to come and gather around each person (two or three around each is good) and pray for that person's ministry. Don't allow time to take requests. Just have them pray God's blessing and power into the minsitry.

2. Invite the people in the room to spend time praying through your sanctuary. Invite some to pray:

through the seats--that God would open the hearts of those who sit there, etc.
around the pulpit--that the power of the Holy Spirit would fall on those who preach from the pulpit.
where the worship team stands--pray for passion in worship, that they would lead people into God's presence.
next to the altar--that people would respond to God's word, be responsive to the wooing of the Spirit.
where the offering is taken--that God would make people cheerful givers.

3. Have elders pray for the spiritual hunger for people. Have those who attend come to the altar. Then have elders pray out loud for the spiritual health of the congregation.