Ordinariate compline may be found at page 179 in The Book of Divine Worship (Newman Press), which, however, will in the near future be replaced by a new liturgical book common to all the ordinariates in the world. For a complete Coverdale psalter pointed for the Gregorian tones you may want to invest in St Dunstan's Plainsong Psalter, published by the Lancelot Andrewes Press, from whom it may be had. There is no other book to compare to this one, Coverdale or otherwise.

I have yet to see a Catholic attempt at using the Gregorian tones for English psalmody that did not get the syllabification wrong, or in one way or another botch the tone by putting two syllables on what is supposed to be a podatus, or putting one syllable on two neumes that are supposed to have a syllable each, or some such amateurishness. Anglicans have been doing this for quite a long time and are much better at it. Get the St Dunstan's Plainsong Psalter.

Thanks for your commentary, Father. I was remembering examples that I had happened to have seen over the years, but cannot, right now, offer specific ones. Although I did say 'I have yet to see...', perhaps I erred in overly generalising. Everything you say is, of course, true. It is, though, quite possible to sing English psalmody to the Gregorian tones without altering the tone or its implied syllabification. Too, one may observe that sometimes this results in an accented or unaccented syllable where, technically, it doesn't belong in a given psalm tone. When this happens, some artful locution and musicianship are required to produce a graceful result. One might, also, offer the general experience that the Coverdale psalter is rather easier to work with in this regard than many modern translations, this owing to its generally more graceful and less abrupt language.

Actually, we should have for our use a revised Grail psalter set skillfully to the Gregorian tones. This would be a worthy companion to the St Dunstan's Plainsong Psalter, which is Coverdale's version. There is no reason at all why Catholics can't do this, and do it skillfully, it's just that they never seem to do so; it's always the Anglicans who seem to fill such voids.

Um, these 'Anglican prayer-book services' are now quite Catholic masses and offices, in case you haven't heard. And, as to the matter of the antiphons, I see no universal problem to matching a psalm tone to its respective antiphonal mode... except that, admittedly, some of the more elaborate cadences do present problems in an English that is too abrupt and relatively colourless.

And, psalmody has many uses and benefits other than as in its role in the divine office, in which it is graced with antiphons. Such unison singing is profitable both spiritually and musically at choir rehearsals and gatherings. (Indeed, a choir that cannot sing well in unison isn't really ready for part singing.) Singing psalmody as a classroom devotional or musical activity should have great spiritual appeal and catechetical value to students, who can learn untold riches from it. While many households say the office daily, others might find great reward in singing the psalter together. The psalter itself is a prayer book and singing, rather than merely 'reading' its contents is a source of great spiritual joy not to be dismissed easily. I quite often sing from the psalter in a wide variety of situations. Psalmody has almost endless uses and pleasures outside the divine office and other rites wherein there are appointed antiphons.

My apologies for being defensive. Please forgive.
There are no settings of any antiphons in St Dunstan's Plainsong Psalter. It is strictly a psalter, except that it does have Magnificat and Nunc Dimittis psalm tone settings, as well as a few other canticles, in all the eight modes, plus the four Marian votive antiphons and their collects in English to the historic Gregorian melodies.

Um, I think simple, not solemn.

Folks, I just found this little gem. Can anyone tell me what the numbers above parts of the psalm texts mean?
https://archive.org/details/TheOrderOfComplineThroughoutTheYear

MJO - Thank you so much!

You've saved me a lot of stress and strain!