Chrysobothris chrysoela...

At the risk of opening a Pandora's box, there are rules for pronunciation of scientific names, but you will get disagreement (sometimes passionate) from entomologists over specific examples because 1) incorrect usage may become "established" as correct, 2) the derivation of a word (and hence its proper pronunciation) may be uncertain, or 3) "that's not how I learned it".

With that disclaimer out of the way, I presume oe to be a dipthong and thus pronounced è (grave accent indicating a long vowel sound). As a result, strict interpretation of the rules would dictate that Chrysobothris chrysoela be pronounced "krì-SÓB-ó-thrís" "krì-SÈ-luh" (acute accent indicating a short vowel sound). This genus, however, is a perfect example of incorrect usage becoming established as "correct". The antepenult syllable should be accented, since the vowel of the penult is short and followed by a mute and the letter l or r (in this case, -thr-), but most people (buprestid specialists included) pronounce it as "krì-sò-BÓTH-rís".

Few entomology texts (or biology texts in general, for that matter) provide any guidance on proper pronunciation of scientific names. However, An Introduction to the Study of Insects, by Borrer, Triplehorn, and Johnson contains an excellent and very readable synopsis of such - I highly recommend it!

p.s. - Nomina Nearctica is rife with spelling and nomenclatural errors. It's okay as a general reference, but I wouldn't rely on it too heavily as a final authority.

p.p.s. - maybe this was way more information than you wanted, but I actually like this kind of stuff!

as omicron eta which we don't think would be a diphthong, but interesting!

...oe is not a Greek diphthong, thus o and e would be treated as separate syllables. Since latinization places the accent on the antepenult if it is long (as eta is), the pronunciation would be "krì-sò-È-luh".

But that's not how I learned it :-)

"Since latinization places the accent on the penult if it is long..." ?

Or did you mean to put the accent on the third-last syllable instead of the second-last?

...not antipenult.

I seem to have made a mess of this one ;-)