As far as UK and US popular press evidence goes, for 'swear blind', use of the verbal phrase, where 'blind' modifies the action 'to swear', is found as early as 1886 in the UK, and 1909 in the US. Use of the expression was much more common in the UK, at least as found through the first decade of the 20th century.
Derivation of the verbal phrase seems to be from emphatic shortening of common earlier set phrases with adjectival use of 'blind' modifying [something] (rather than modifying the verb 'to swear'): "swear blind [obedience, allegiance, fealty, etc.]". The adjective "blind" in the fuller expressions was sometimes paired with another adjective; for example, "swear blind and unreasoning obedience".
The reason 'swear blind' is more common in the UK, and appeared so much earlier in the popular press there, may be sociological. As speculation, while a tradition of blind, unreasoning loyalty is an established cultural feature of any kingdom, that same tradition has less force in the more individualistic US, particularly after the revolution.
The phrase 'swear up and down' in early use always involved either [something] sworn to, as in "swear [something] up and down" or "swear [something] up or down", or it involved motion, as in "he swore up and down the veranda".
For example, the earliest use of "swear up and down" I found in the popular press took the form of "swear up and down [to somebody] [that something is true]":
I have heard travellers who had encircled the globe, swear up and down to enthusiastic young lades in morning walks, that the scenery of this that and the other place, where they happened to be, was not to be surpassed anywhere in the world.
Burlington Weekly Free Press, Burlington, Vermont, 21 Sep 1855 (paywalled).
The use of 'to swear up and down' or 'to swear up or down', if it does not derive from the motion of the swearer (as in the earlier-mentioned "swear up and down the veranda"), derives from a peculiar practice once (apparently) only too common. That practice is described in an early diatribe:
But the more barefaced evil of all is the toleration of a set of men called swearers or valuators, in every country, to swear up or down the franchise, according to circumstances. There is a regular corps of these attached to every staff: dismissed or broken down Process-Servers — disinherited Commissioners of Rebellion, whose "occupation's gone," and are now ripe for anything. A set of fellows that would swear the bark off of a tree, or the cross off the back of a Jackass...And yet these are the fellows who are absolutely tolerated in a Court of Justice — whose damaged oath will be taken against the consecutive and unimpeached testimony of twenty irreproachable individuals; and, contrary to all principles of law and equity, the brand of perjury is fixed on numbers by the purchased evidence of outcasts of the kind.
Dublin Evening Post, 12 November 1839 (paywalled).
Initially, the phrase with reference to the practice of swearing [something] "up or down" was only "up or down"; it later developed into swearing [something] "up and down":
If, instead of abusing the judges, litigants in the Land Court would produce witnesses who are known to have a "practical" knowledge of land, and not "horse marines," who swear up and down as suits their clients and as prices rise and fall, decisions would be much more likely to be fair than they are now.
Dublin Daily Express, 27 January 1888 (paywalled).
Early uses of 'swear up and down [that something is or is not true]', or 'swear up or down [etc.]', in the US included uses referring to paid perjury, just as in the UK. For example,
It was stated that there are persons, mostly from the centre of Europe, who let themselves out to swear up or down a case; and Mr. Read, a counsellor, remarked that such uncertainty exists as to testimony which may be manufactured and brought up against their clients that members of the bar are almost afraid to bring suits.
The Times-Picayune, New Orleans, Louisiana, 05 Jul 1856, reprinted from The New York Evening Mirror of 26 June (paywalled).
A vestigal sense of swearing something up or down (true or false) remains in the set phrase "swear up and down"; however, the more influential derivational sense (although still vestigal) seems to be the sense of 'swearing-in-motion', as in "he would advise any slave to swear, up and down, that his master was a secessionist" (The Liberator, Boston, Massachusetts, 24 Jul 1863; paywalled). That this is the more prominent derivational source is especially evident in a later elaboration of the phrase, wherein things are sworn "up, down and sideways" (mid-20th century).
I speculate that the reason 'swear up and down' appears more frequently in the US may be that the sense of 'swear up or down', referring to paid perjury, was less common in the US, and was associated in the US with European practices (see quote). Thus, the development and adoption of the phrase 'swear up and down' encountered less interference from the conflicting sense of 'swear up or down' in US use than in UK use.