The various combinations of omicron and epsilon with circumflex are not a feature of "standard" Greek, and so precombined codepoints for them will likely never be added to Unicode, as the official policy of the Unicode consortium is to recommend the use of combining diacritics for these and other characters. So the official answer is to use omicron + circumflex, and it would certainly be preferable to use the correct Unicode codepoints than some non-standard ones such as those used in the Private use area of some fonts (e.g. Cardo).
|ο͂||U+03BF U+0342||omicron with circumflex||ο͂|
|ε͂||U+03B5 U+0342||epsilon with circumflex||ε͂|
|οͅ||U+03BF U+0345||omicron with iota subscript||οͅ|
|εͅ||U+03B5 U+0345||epsilon with iota subscript||εͅ|
|ο͂ͅ||U+03BF U+0342 U+0345||omicron with circumflex and iota subscript||ο͂ͅ|
|ε͂ͅ||U+03B5 U+0342 U+0345||epsilon with circumflex and iota subscript||ε͂ͅ|
On the other hand, not all fonts display combining diacriticals very well yet, since the technology for mapping two codepoints to a single glyph is not well executed on all systems. (This capability is assumed in the Unicode standard, and using OpenType and other related technologies it is possible to design a single glyph to be displayed when a particular codepoint combination occurs, so that e.g. the circumflex harmonizes with the omicron, rather than merely appearing to be overtyped - but executing this technology in operating systems and in fonts has not been a priority for commercial programmers and typefounders.) So what do we do when we want to display omicron-circumflex?
What the Aphrodisias project has done (e.g. ALA 117) is to use combining diacriticals. Unfortunately this does look a little bit awkward, as some font designers did not bother checking if the precombined circumflex and the precomposed letters with circumflex match. For most cases and uses the end result will be acceptable. Note that the right character to use is COMBINING GREEK PERISPOMENI (0342) and not COMBININING TILDE (0303) although the glyphs might be the same in some fonts.
An update about the behaviour of different operating systems, browsers etc. will follow shortly.
Notis Toufexis in cooperation with Gabriel Bodard.