Rock climbing isn’t something I’ve heard of much on Islay, as far as I can tell there doesn’t seem to be much opportunity to do it. Nevertheless Roger Brown did just that (with a stopover on Skye for some more rock climbing) and made a video about it:
Some of it seems to be near Port Wemyss on the Rhinns of Islay, not sure where the rest was. May be on the Oa or at Sanaigmore? There are certainly some steep and impressive cliffs at both locations.
I hope you enjoyed the video, I found it very interesting (and a bit scary) to see them climbing above the waves rolling in at the steep cliffs.