Well, in Morrowind you could go through Daedric Ruins. There were pieces of Daedric language in there. 

I don't get your confusion, Seb.

I remember those ruins. Good old Morrowind.

And the Oblivon Gates may not have exactly have been inscripted, inside Oblivion you could find numerous etches scattered throughout the place. 

I don't get Seb's confusion as well . . .

UPDATE: The Daedric Translator isn't any good.

DUN DUN DUUUUUUUUN...

Well, now we have a new dilemna: Where did my cocoa go? *the sound of drawers opening and angry muttering* SLAM! 

Well, I guess I'll go get a napkin. Ummm... I'll get back to you on your dilemna, right now the rats are circling.

There is the alphabet of the Daedric Language, but no actual, fleshed out language is there? I think it'd be a good idea for Bethesa to work on that language, then who knows? Maybe the language would be added to this site or an alternate site to learn.

Unfortunately Bethesda has been turning more towards the elves, Akavir, and the Empire. More so than ever before. But the daedra will never be irrelevant. That much is for sure.

Sadly there does not seem to be a cut and dry way of getting past that problem, but there is an alternative. Hopefully a temporary one. 

It is correct that the Altmer came from the higher planes, the Aedra, and with it their language, which later brings the rest of the elves with them. Each of their languages stem from the Aldmer language, Aldmeris, but there is an ancestor prior to that, known as Ehlnofex, spoken by the Ehlnofey, which constitutes the building blocks of most of the languages spoken throughout Tamriel; Tamriel itself being Ehlnofex in origin, meaning Dawn's Beauty.

Aldmeris, Nedic, Draconic and Akaviri are the children of Ehlnofex. If there's enough information from all four languages, one may be able to contruct a crude but close version of the language we're looking for. More than likely the language wouldn't pertain to just Daedra, but would pertain to Aedra and other such beings as well. More than likely the first language, a universal one. Example, think of this problem being the tower of Babel. 

Hope that helps and hopefully Bethesda does that legwork so we don't have too. Was hoping to make a fairly accurate tattoo displaying both Draconic and Daedric language, but I suppose I'm shelfing that project for another day.

Sources: Various playthroughs of each TES games and various wikis.