There is some information on booking a table via the Taverni Agni link. This explains:
You can reserve an evening table from 7 pm till 10.30 pm
Lunch from 12 noon till 3.30pm
To reserve a table, Telephone Taverna Agni on:
0030 26630 91142
Please note, we have now stopped taking table reservations via email or online.
We only have one sitting and thus you may stay at your table for as long as you like. Tables are allocated on a time based system. Those arriving early, will be seated closest to the front.