The first quote comes from At Home and Abroad: A Sketchbook of Life, Scenery and Men by Baynard Taylor and is vivacious:
There was the same lithe,
wiry frame, unworn by much endurance, the sloping brow,
expanding to a wedge-like shape at the temples, and the
quick, keen, vivacious gray eye, as I remembered them in
I can't find all the other quotes online but where they are not found it's entirely likely that they are a misreading of vivacious too. Optical character recognition may miss the very thin tail of c, only registering the left-hand thick stroke and terminal ball or serif and mistaking it for r.
The quotes which are obviously and verifiably correctly vivarious — that is, Umberto Boccioni, Westerly and The Scrinium — all appear to mean simply living.
The word does not appear in OED, which is testament to its rarity: even OED can't list every word used in print, although I would have expected the three examples here to be enough to trigger its inclusion.
The viv- comes from Latin vīvĕre, to live; and OED does list the -arious suffix:
< Latin -ārius, -a, -um ‘connected with, pertaining to’ + -ous suffix (as if < Latin -āriōsus; cf. cariōsus, carious). The reg. English repr. of -ārius is -ary suffix1; but the compound suffix is of occasional use, as in cibarious, gregarious, temerarious, vicarious, and as a by-form in arbitrarious, contrarious, etc. (Hilarious, < Latin hilari-s + -ous, seems to owe its form to association with this suffix.)
That being the case, I don't believe the writers intended vivarious to mean "pertaining to life" as one might say that a [warm-blooded] animal has a vivarious warmth — it's warm while it's alive. I believe they have mistakenly coined the word and it would have been better to have been vivarous, where the -ous suffix derives from Latin -osus. From the OED again:
< classical Latin -ōsus (-a, -um), forming adjectives, with the sense of ‘abounding in, full of, characterized by, of the nature of’, e.g. cōpiōsus copious adj., dolōrōsus dolorous adj., fāmōsus famous adj., generōsus generous adj. and n., glōriōsus glorious adj., spīnōsus spinous adj., viscōsus viscous adj., etc.
Vivarious is comfortingly similar to vicarious, which might explain why that form was chosen. Tim Lymington has posited that Edridge may have intended viviparous in The Scrinium.
It's entirely possible that OED also believes vivarious to be a mistake, which is why it's not included even though there are probably sufficient instances to warrant it.