or would it be:

*amiltoron
*atartoron

*amilleþeler > amilleseler
*atarþeler > atarseler

For me in a compound the first element is the modifier, the second is the principal so something like *néþatar to me means "sister-father" whatever that is.

and then:

*hánion n. nephew
*hániel n. niece

*néþion n. nephew
*néþiel n. niece

Many of the above feel a bit clumsy to me, but the last set (hánion etc.) are not bad. Perhaps we should also look at the various EQ and G formations for 'cousin' which may give us a clue how we could approach these removed relations.

It seems forms of rendo and resse are found in G. to mean close but distant relationships cf. bethren brother-in-law, bethress sister-in-law. So maybe *atarendo/sse, *amillendo/sse? (though, amillesse looks like a locative of amil(le).

*verrendo, *verresse

I go for your second suggestions (the amiltoron row of words). Actually, I don't know where those obscure *háno and *néþa come from, I use toron and þeler all the time :).

+Andre Polykanine both háno and néþa are well attested in Tolkien's essay on Eldarin names for fingers and numerals in VT47.

+Tamas Ferencz Does it invalidate toron and þeler?

+Andre Polykanine no, I would not say that. Treat them as synonyms.
Paul has written an analysis of the roots and words related to brother and sister, it's well worth reading: https://plus.google.com/101464290458691045803/posts/cygRdTHV4tz
plus.google.com - Here is another exploration of Eldarin words, this time “father/mother, son/d...

OK I have pondered this and I think I can pinpoint now what my problem is. Compounds like *atarnéþa etc. are semantically fine, and could be adopted into NQ, but they feel almost like technical terms - they describe the relationship but I don't think they are words one would necessarily use in day to day situations ("hey, Túro, atarnéþa Serinde called, she is out of sugar, would you go over and get her some? atarháno Valion is ill, he can't go to the shop").
Or maybe they are, I don't know. But looking at IRL languages, in many of them words for aunt and uncle are not just used for the specific paternal or maternal relations, but are also generic terms for (elder) women and men. I feel Quenya could have something similar, if we could come up with something that feels realistic.

Good point, +Tamas Ferencz! Interesting enough, that there exist languages that have this distinction, but the words tend to be shortened. See Swedish for example: the "proper", so to say, etimological forms for father and mother are fader and moder, but they are commonly shortened to far and mor; brother is broder (shortened to bror), and sister is syster (not shortened). And: maternal uncle is morbror, paternal uncle is farbror, maternal aunt is moster (note! Syster is not shortened, but ** morsyster is non-existent, as far as I know), paternal aunt is faster. And you'll guess on your own who are mormor, morfar, farmor and farfar :). BTW, my Swedish is not too good unfortunately, so I don't know if there exist a general term for an older man/woman, like Russian дядя and тётя, for example, which can refer either to parents' siblings and their spouses or colloquially to anyone, especially when addressed by a child. And thanks for the link to Paul's post, I don't know how I missed it.

Maybe we should just use háno atarwa etc.

+Andre Polykanine well perhaps I was a bit too harsh on those neologisms, because if I think of it, in Hungarian the word for cousin is unokatestvér which means literally "grandchild-sibling" on the account of them having the same grandparents. (We also have kuzin probably from German, but that's rarely used).
But for aunt/uncle I think it would be really nice to find/coin some generic terms.

+James Coish indeed that's failsafe and can work in many situations.