Chamber musicians generally run into the same sort of issue -- and, in fact, even if you do have a drummer, this can be an issue.
In the better groups I have played in, solutions have boiled down to three things:
- Each musician must be able to perform his or her part alone, in time. That means practice with a metronome, working toward the tempo that the group will use in performance.
- The group as a whole must practice together, often using a loud metronome, to stay in time. If you need earbuds, fine, but a sufficiently loud metronome (such as Dr. Beat) should also work. You might need to hook the metronome up to an amplifier or speaker of some sort so that everyone can hear it. Note that if the group tends to "lose" the metronome in practice, you probably need to slow down the tempo as a group, using the metronome, to make sure you can stay together at some tempo before gradually speeding up to the performance tempo.
- The group needs to communicate visually. That is, make sure you look at each other whenever possible and appropriate. An added benefit is the impression to your audience that you are engaged as a group and -- just maybe -- you're enjoying your performance.
In serious chamber groups (saxophone quartets, in my case), this process took a large portion of our rehearsal time, possibly more than any other single aspect (though intonation work is likely close).
In a different genre/medium, I think some of the same things would still apply. The musicians need to be able to keep time on their own as well as within the group. Check with a metronome often to ensure that you are maintaining the correct tempo in practice. When you get to performance, ideally, you are not using any external time-keeping device.