One way to do this is to use eight MB-4E mini boundary mics. These tiny, low-cost units have a half-supercardioid pickup pattern which reduces pickup of room acoustics. They come without a connector, ready to solder to a connector that mates with a transmitter.
Left: MB-4E. Right: MB-4.
You'd need one transmitter and one receiver per microphone. Mount each transmitter under the table, and mount each receiver in your audio rack. Run the eight receiver outputs into a gated mixer, which turns off mics that are not in use. This greatly increases clarity.
Another option employs eight MB-4 microphones, a gated mixer, and one transmitter/receiver. Each MB-4 mic has an XLR connector, which plugs into a gated mixer with eight XLR mic inputs. Mount the mixer under the table. Feed the mic-level output of the mixer to the input of a wireless transmitter mounted under the table. In your audio rack, connect the receiver output to your audio system amplifier/recorder.
Place each microphone on the table at arm's length from each person, or between every two people. Mount each mic with the included double-sided tape. Drill a hole in the table behind each mic to run the cable through. Since the mics are small, caution the participants not to cover the mics with papers.
Inside the MB-4's XLR connector is an equalizer circuit that boosts the bass for a more natural tone quality. This circuit is omitted from the MB-4E. So if you use MB-4E mics directly into transmitters, the bass will sound a little thin unless you boost the bass on your mixer.
Once this system is wired up, you'll have a convenient, portable conference table with built-in microphones.