Indeed this is one of those simple words that seem to be mm missing from all of the languages. I am still hunting...

I don't think **colil would work. That syllabic L which is behind the suffix followed stops like t, k, not l.

There appears to be an old Qenya word poko "bag" in PE12:75 which could provide ground for ideas like S *pôg, col⁽ʷ⁾-/cúl-bog (vs. -phog).

- ô pro û, due to OS *-o as in brôg, pôd

Indeed I have just found poko in the Quenya Lexicon myself, too. I think we can add the NeoSindarin cognate to VQP

Eglerio i mellyn vaer hin! Thank you!

So, a suitable name made from pôg, but which is not too similar to the verb pog-... And I have the idea that  the initial B in Bilbo might be a P in a sindarin version, both for the allitteration and because I believe that reflects the sindarin phonology better. Ideas?

+Hjalmar Holm why does an initial P reflect the S phonology better than an initial B?

I found more words with initial Pi- than Bi-, but really, it was more of a question, a thought. Sorry if it sounded like I know what I'm doing.

Might Pôgion be a translation for Baggins?

+Hjalmar Holm
Just remember that when you combine (monosyllabic) words that have a long vowel into a compound, the vowels shorten, as in

gîl + dîs = Gildis
mîr + tân = mírdan
hîr + iôn = Hirion ("son of lord")

so pôg would also contract to pog-.

* Pog-ion might work, unless another (adjectival/agental) element like, say, –ben (WJ:372, 376) should click even better; let us observe that Westron Labingi "Baggins" resembles at least superficially certain Germanic forms, especially ON/Icelandic weak masculine nouns of the type ættingi "kinsman", foringi "leader" (this –ingi is of the same origin as Old English genga "(fellow-)traveler, companion" in A Handbook of Germanic Etymology, p. 126).

ܤܡܝ ܦܠܕܢܝܘܤ
Thank you! -ben might be better, as you say.
 

Proposed to me was this, as a translation of Baggins: "Baggins": *Pogodion - Son of Little Bag (*pôg+-od+-ion).