おいでやす is Kyoto-ben for いらっしゃい and is used by shopkeepers to welcome you in the same way. However there are a lot of kyoto-ben expressions ending in やす so I've been trying to find out what it means. So far, after a web search, I've only found something usable in a paper comparing the origins of Japanese with Korean, which states the following citation:
Maeda’s (1961:149)
explanation using de yasu, which is assumed to derive through de arimasu →de (ari)yasu →d(e y)asu →dasu.
I'm therefore thinking that yasu might be an archaic form of arimasu and therefore means to exist. (Caution: Wild guess)
Now oide means 'to come here', 'in' etc. Rakaichan also has 'being in (somewhere)'
This would give us, '(you) exist here'.
Now irrasshai is the exalted form of iru (to exist/be located) so this also is that stating that you exist, which makes me hopeful that my guess about 'yasu' is correct.
Another possibility that occurred to me were that it might be related to 'dasu'. I don't think it's related to 'desu', since Kyoto-ben has 'dosu' for that.
Any thoughts?