Polish, so I've read, has the following syllable-templates.
One-syllable words are (C)(C)V(C)(C).
Word-Initial syllables are (C)(C)V(C).
Word-Final syllables are (C)V(C)(C).
Word-Medial (i.e. all other) syllables are (C)V(C).

Perhaps that's wrong; perhaps it's close to right but needs modification; 
perhaps it's "right" but there is/are another (or some other) analys(i,e)s that 
are equally "right".

STRESSTYP does appear to contain several languages whose syllables have 
mandatory onsets, though it doesn't contain any whose syllable-template is 
CV.  (I understand Hawaiian and Mba are CV languages, though.)
Embera Saija; Epera Pedée 
Gooniyandi; Gunian; Konejandi,   
Hebrew, Tiberian 
Khmu' 
Masset Haida; Northern Haida 
Puluwatese; Puluwat 
Wardaman 
Yele; Yeletnye 
Zoque, Copainalá 
Aceh Atjeh; Atjehnese; Achehnese, Achinese) 
Kewa 
Khmer, Central; Cambodian 
Kutenai 
Kuuku Ya'u 
Pokomchí; Poconchi 
Senoufo, Supyire
Slave


STRESSTYP says their language #225, Kunjen (Australian, Pama-Nyungan, 
Paman, Central Pama: Cape York Peninsula (Aus)) has mandatory codas and 
no onsets; its syllablle-template, they say, is
VC(CCC)
though I doubt that all coda-clusters reallly have to be exactly four 
consonants long; they probably meant VC(C(C(C)))) or something.

They give the syllable-template of "Arrarnta, Western; Aranda, Western" as 
V(C)CV(C)...
which I think must be some kind of typo; so from STRESSTYP I can't confirm 
that Arrarnta/Aranda syllables require codas or prohibit onsets, though clearly 
they don't require onsets.

I couldn't find any other languages in STRESSTYP that it says have mandatory 
codas; I found forty-five languages that it says have VC in their syllable-
templates, but I couldn't review all of them in the time I had.  All that I did 
review, however, also have open syllables.