Typing these characters is fairly straightforward, if you have an appropriate keyboard (or can customize yours): they're simply the lowercase Latin letters <e a o>, followed by the character U+032F Combining Inverted Breve Below. This second character can't be copied and pasted on its own, since it's combining, but it should be available in any decent IPA keyboard (such as this online one). In TIPA (the standard way to type linguistic symbols in LaTeX), you can use the \textsubarch
macro (\newcommand{\htwo}{\textsubarch{a}}
or the like).
The reasons for using these letters are a bit more complicated.
First, I'll provide a basic summary of what the laryngeals actually are. (OP obviously already knows this, but it makes the answer more useful to others.)
It's generally agreed that many Proto-Indo-European phonemes could appear as either consonants or vowels. In particular, *r *l *m *n *j *w could all appear in both ways. This is why it's sometimes claimed that PIE had only two vowels (*e *o) when various reconstructions appear with *i *u: the *i *u were the vocalic versions of *j *w, which are seen as consonants first and foremost.
A PIE root, at its most basic, consists of two groups of consonants. For example, the root *bʰ_r means "carry", while the root *l_jǵ means "bind". In between these two consonants would be placed either a short vowel *e or *o (short grade), a long vowel *ē or *ō (full grade), or nothing at all (zero grade). And in the case of nothing at all, one of the consonants would often end up becoming vocalic to make it pronounceable.
But linguists found some roots which didn't seem to fit this pattern. Some of them had no consonant at the end, like *d_ "give", while others had no consonant at the beginning, like *_d "eat". And the ones with no consonants at the end, didn't seem to follow the normal ablaut patterns. "Give", for example, only ever appeared with *ō, which was never short or replaced with *e.
The current view is that these changes were caused by "laryngeals" (which have nothing to do with the larynx but the name has stuck). There were (at least) three of them (*), *h₁ *h₂ *h₃ = *e̯ *a̯ *o̯. When they appeared next to an *e, they would "color" it into their respective vowel. If they appeared after a vowel and before another consonant, they would also make the vowel longer. Then, in every language besides Hittite, they would all disappear. So the root for "give" wasn't actually *d_, but *d_h₃ = *d_o̯.
(*) Some scholars say there were more, maybe as many as five, but this theory isn't widely accepted. I haven't seen any modern reconstruction with less than three.
Writing the laryngeals as *e̯ *a̯ *o̯ certainly does seem more elegant, especially by analogy with *j *w sometimes being written *i̯ *u̯. But it's unclear how good this analogy is.
When the consonants *j and *w are left on their own (in the zero grade or for other reasons), they appear as *i *u. Other consonant-vowel pairs seem to have done the same. This is quite uncontroversial: for instance, *nj-sd-os "nest" surfaces with an /i/ sound in most descendants (see Latin nīdus).
However, when the laryngeals were left on their own (i.e. with no adjacent vowels), they disappeared in almost all descendants. Greek alone shows the reflexes /e a o/. Latin, for instance, shows /a/ for any laryngeal left alone between two consonants, while "proper" PIE *e *o within roots survive. To me, this is convincing evidence that *h₁ *h₂ *h₃ were not the consonantal equivalents of *e *a *o.
It's possible that they did have vocalic equivalents (sometimes called the Schwa Indogermanicum and written *ə₁ *ə₂ *ə₃), but it's also possible that they didn't: the branch that eventually became Greek might have inserted some sort of epenthetic vowel next to laryngeals, which then got colored. But it seems clear that, if they did have vocalic equivalents, they were not the same as the vowels *e *a *o.
As such, I wouldn't recommend using these symbols. They're certainly more elegant and easier to read than *h₁ *h₂ *h₃, but the false analogy with *i̯ *u̯ seems too dangerous. Instead, they might perhaps be written *ĕ *ă *ŏ? But I don't believe this has ever been done.