The United States of the Ionian Islands was formed on 14 November 1815 and was made up of seven principal islands: Corfu, Cephalonia, Zante, Santa Maura, Ithaca, Cerigo and Paxo. These islands are represented by the seven arrows held by the winged lion of St. Mark (a Venetian symbol reflecting the Venetian control of the islands from 1401 until 1797).
The Obol was equivalent to an English halfpenny, so the Two Oboli coin is listed as "One Penny" in some sources. It is also known as a "diobol" (double obol).
Coins were minted at the Royal Mint in London and, like the rest of the coinage with the exception of the 30 Lepta coins, do not indicate the denomination in any way.
On some coins there is a dot after the date and on some there isn't. However, this doesn't seem to be a mint mark. According to Remick's Guide and Catalogue of British Commonwealth Coins, some of the Ionian coinage was struck at the Ralph Heaton and Sons mint in Birmingham, but there is no indication which. The Greek Wikipedia entry on Ionian coinage only shows Birmingham one Obol (five Lepta) coins.