A few of the Co-ops such as the Irish Agricultural Wholesale Society, Kerry Coop and Avonmore, seemed to hive off their assets into Plcs and issue shares to their members.
Brendan is correct by saying its a technical area. The reason being is that Co-Ops are incorporated and governed by The Friendly Society whereas Limited Companies are governed by the Companies Registration Office. To the best of my knowledge, i don't know if you can convert a Coop to a Ltd Co. I think it would involve something along the line of striking off the CoOp and registering a new company.
If you contact The Friendly Society on Parnell Square, they should be able to tell you more.