Not exactly where the Co-op was (that's the Garrick Snug) but further down towards Allinsons, on the corner at 110 Grange Road.
Now under part of the Market Hall. There is more on Wiki here - Link.
At the top of Grange Road was the Grange Hotel. Again, more on Wiki here - Link.
There is a page on this site which indexes all the known pubs, within 'Wirral Pubs Past & Present'. If needed, you can use ctrl+f (control f) to search through the list as it's not in alphabetical order.