The usual spelling is Eilís which can can be pronounced Ey-lish or Ay-lish. Ailís would be Ay-lish - I have never seen this spelling though I have seen Ailish - an Anglicisation of Eilís.
I have never come across Ailis(no fada) but it would be Ay-lis. However I would not be surprised to find an
Ailis calling herself Ay-lish - Irish people are not always strict about applying fadas(accents).