Shogakukan does list the 難有 combination with a reading of ありがた in one place, in the title of a kabuki play: 難有御江戸景清. Poking around online suggests that this is read as ありがたやめぐみのかげきよ. The reversed kanji order would match Chinese syntax better than Japanese, making me wonder if this is simply a kanbun style of spelling.
Googling a bit more brought up this OKWave Q&A wherein the "best answer" claims that this is originally the spelling for かたじけなし, changing in meaning over time to be ありがたい and then used with that reading. However, the etymology for かたじけなし does not seem to have anything to do with 難い, at least according to Shogakukan, and using 有 for なし seems far too much of a stretch.
This goo thread seems to confirm my suspicion, that 難有い is simply the kanbun + kun'yomi spelling of 有難い, as suggested by their kanbun example of a different word using 難い where the 難 kanji comes first in the spelling, but the かたい reading comes second in the pronunciation.