Garmin map of Iceland
Your best bet for a Garmin map of Iceland is to go to http://garmin.openstreetmap.nl/ and select Iceland from the Europe list.
Alternatively a map can also be obtained at http://garmin.opentopomap.org/.
An older map from ~2014, which seems to have more PoIs and seems not to be OSM based, is also provided from http://www.ourfootprints.de/gps/mapsource-island.html (a page in german). You can find the download options at the bottom of the page.