Like Billina, I also see "ass sling" when I look at this name. Visually, it's just...not pretty, and I can't say I'm crazy about the "ling" sound at the end, either. I prefer Aisling over Aislin since it makes the pronunciation clearer.
I'm not usually an advocate for invented names, but I find ASH-lin far more attractive than ASH-ling, and I'd take Ashlyn over Aisling or Aislin any day.