Good question! I wasn't able to find any unambiguous examples either with a short search, and I found one source that says there are no known examples of languages with only CV syllables.
Understanding Phonology (Fourth Edition), by Carlos Gussenhoven and Haike Jacobs, says:
The onset may be obligatory. Languages with obligatory onsets are not hard to find, like Arabic, Dyirbal, and Klamath, but languages that allow only CV, i.e. an obligatory onset followed by a monomoraic vowel, must be rare, to the extent that we have no example. Analytical issues may arise from phonetic onsets in onsetless syllables. Many languages, like German, regularly have a glottal stop in these contexts, as in [ˈafə], pronounced [ʔafə], 'monkey', while in Mba and Ndunga word-initial high vowels appear to be variably preceded by [ʔ], [ɦ] or a homorganic semivowel (Pasch 1986: 32, 91). Henan Mandarin has a homorganic semivowel preceding a non-low onsetless vowel, as in [i214], pronounced [ji], 'one, numeral'; [y41], pronounced [ɥy], 'fish'; [u341], pronounced [wu], 'house', [ɤ341], pronounced [ɰɤ], 'hungry'; and a glottal stop before low vowels, as in [æɛ341], [pronounced [ʔæɛ], 'love' (personal field notes, CG, 2014). Phonemic glottal stops are easily distinguished in languages like Hawaiian, where they contrast with empty onsets, as in [aa] 'jaw' and [ʔaa] 'fiery' (Elbert and Pukui 1979), or Arabic[*see my note below], which has the same contrast in the coda of the syllable and has the glottal stop in the onset within words, as in [lawʔa] 'sorrow' (Thelwall and Sa'adeddin 1990). German has none of these three properties.
I think it will be hard to find clear answers to this question because for theoretical reasons, in ambiguous situations a CV analysis is often favored over an onsetless V analysis. (In fact, there is even a theoretical tradition of abstractly analyzing languages that appear to unambiguously have non-CV syllables as actually only having CV syllables with empty positions: "Strict CV phonology". So from a certain theoretical perspective, the answer to your question could actually be "all of them"!) This can sometimes lead to confusion when sources don't mention the theoretical basis of analyzing a certain language as having obligatory onsets. (User6726 brought up another theoretical point that can be tricky that I had forgetten about, the analysis of C + glide sequences (or C + coarticulated glide) as phonemes vs. consonant clusters.)
For example (this wouldn't even be a CV-only language anyway, as it allows coda consonants, but just to illustrate the point) Mandarin Chinese can be said to have obligatory onsets, from a certain point of view. But in fact, in Mandarin this is accomplished by analyzing what could be thought of as vowel-initial syllables as starting with a "zero onset" that has a variable realization, and can be [ʔ], [ŋ] or [ɣ]. This is mentioned in Syllable Structure: The Limits of Variation, by San Duanmu, 2008 (p. 73). In fact, Duanmu expresses doubt about this analysis and ends up saying "In summary, the zero onset effect in utterance-initial position is probably unintended, and in medial positions there is no evidence for the zero onset or for resyllabification across a word boundary" (p. 76).
I would imagine that in many languages that are said to have "obligatory" onsets, some of the onsets might be consonants that could be seen as epenthetic in at least some contexts, such as glottal stops or glides that are homorganic to the following or the preceding vowel.
Even the examples given by Gussenhoven and Jacobs of languages with obligatory onsets are not all entirely straightforward. Arabic has glottal stop onsets that can be analyzed as epenthetic at least some of the time (see the note below), as well as /ji/ and /wu/. Dyirbal has /ji/ and /wu/, and according to "Revisiting Phonological Generalizations in Australian Languages", by Emily Gasser and Claire Bowern, it is possible that "some writers of grammars [of Australian languages] may have analyzed /u-/ or /i-/ initial words as exhibiting an on-glide, because of the expectation that Australian languages tend to disprefer vowel-initial words. We have no way of investigating this problem with the current data" (p. 7). (I haven't been able to find any relevant further information about the phonology/phonotactics of Klamath.)
These complications certainly don't mean that it is invalid to describe these languages as having obligatory onsets, but they raise some questions about how simple it is to divide languages into two neat classes of "allow onsetless syllables" and "don't allow onsetless syllables" since languages that are often described as having V-initial syllables like English or German may also show similar kinds of epenthetic consonants in the onset of "vowel-initial" syllables in at least some contexts.
* my note: even in (Modern Standard**) Arabic, the situation is complicated in that words that are pronounced in isolation with an initial glottal stop don't all behave the same way in connected speech. There is a phonological distinction between words that start with 'weak' or 'elidable' glottal stop and 'strong' glottal stop.
** I don't know anything about the phonology of glottal stops in the various regional varieties of Arabic.
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