You can of course play Irish music on any diatonic accordion, including a C/F. The problem with a C/F is that you won't be able to play tunes in the keys that everybody else plays them in. So, as Richard says, not recommended unless you want to play solo all the time.
You could get a Lilliput changed to B/C or another Irish tuning by some of the specialists who lurk here. I had one in C#/D prepared by Mike Rowbotham (for someone else, who sold it on). The small size, mainly the buttons and button spacing, took a bit of getting used to, but not much.
Another possibility for a small box is a Castagnari Lily, which you could order in B/C or another key suitable for Irish music. Very compact, but it has only a single voice, which some people find not very pleasant. Well I don't, anyway.
Both these possibilities would cost you quite a bit more than a Black Dot.
As would this intriguing possibility from makers in Switzerland:
click here and then on
Mediumörgeli in the picture. At the top you will see a very compact 19-button 2-voice box with the rows in a 9/10 configuration for "Irisch".
I enquired about this model a few years ago but the price, in Swiss francs, was out of my reach.