I do think that you have it right, the name is most likely spelled Kaniuky or Kaninky on Josef's manifest, the clearer of the two. Most of the stem or root of the name corresponds with the name, Kani(ukai) and "n" and "u" are probably the most commonly mis-transcribed letters in hand-written records like these manifests. The ending "-y" is indeed Polish, which is usually rendered in Lithuanian as "-ai."
The RC churches near the various villages with this name would be in: Pavas^iunai, Alove, or Alytus itself (which had 4 churches.
But I don't think it will matter which one is the correct one if you write an email to the Historical Archives of Lithuania which now houses most available sacramental records from pre-WWI -- if they exist at all. Two of the villages were in the former Russian province or gubernia of Vilnius because they are east of the Nemunas River. The other one was in the Suwalki province, being west of that River. Records from the latter province may be more difficult to track down because of the division of that province between Lithuania and Poland. In any case, the Archives will tell you if they have records for your family since you have their names, their approximate years of birth and the location (even if it only narrows the search down to 3 possible parishes -- I think they'll look in all books from any Kaniukai). Here is the web site for the Archives in English:http://www.archyvai.lt/en/accessandservice.html