Has it ever been formally established that giving any group, X, a
priority of credulity in court over any other group, Y, would amount
to granting the group X a title of nobility?
No. This has never been formally established.
In the 100 years between the ratification of the US Constitution and
"Coffins v US", were there any laws or court decisions which would
give any groups de facto nobility over other groups by demanding that
their accusations against some other groups must be assumed (if
formally stated) true until proven false?
Effectively so. For example, the doctrine of res ipsa loquitor works that way and that have been classes of people who have been historically not eligible to serve as witnesses. There are also many procedural circumstances historically (e.g. confessions of judgment) that operate in this manner.
Did the argument that this amounted to granting of titles of nobility
(which was prohibited) ever come up in any court cases?
No.*
The core litmus test under the title of nobility prohibition has been that a privilege granted by the government is hereditary and is not simply ordinary property. Without a hereditary component, the title of nobility prohibition does not apply.
A lengthy analysis of this jurisprudence can be found in the answer to the Law.SE question "What exactly is a title of nobility?" While this question isn't a true duplicate of that one, the pertinent legal authorities are all discussed in the answers to that question.
- Obviously, it isn't possible to know every legal argument that was made orally in a trial court or legal brief for all of the United States for all time by everyone and anyone, often leaving no historical record whatsoever. There are no recorded appellate court opinions of which I am aware, however, that engage with this legal argument and rule upon it (which is usually what someone really means when they say "did this argument ever come up in a court case").
Post-Script
This post also confounds a "presumption of guilt" with a per se rule regarding credibility determinations, but while both go to the issue of how evidence is evaluated by a tribunal, the two concepts otherwise have nothing in common, and sometimes it isn't clear which is which.
For example, in many U.S. jurisdictions, a marriage certificate in existence at the time someone is born, accompanied by the passage of time under a short (often five year) statute of limitations, conclusively prevails on issues of paternity, over a DNA test that is 99.999% certain to be correct as a matter of genetics.
You could interpret that as meaning that marriage clerks are always more credible than genetic scientists. But, of course, that isn't really the intent. Instead, this is effectively a substantive rule of law couched as an evidence rule.
Similarly, the requirement that real property can only be conveyed in writing could be interpreted as an evidence rule, but it is more realistically viewed as a rule concerning the definition of what a transfer of real property really is that is useful to make a bright line rule. Thus, an oral statement can be a promise to transfer real property, but it doesn't really happen until there is a signed deed or other conveyance.
A traffic ticket basically has a presumption of guilt in some jurisdictions, because if you fail to appear you are found guilty in absentia even without evidence, something that is not permitted as a matter of criminal procedure in the U.S. for more serious offenses for which you can be incarcerated. But, on the other hand, if you do appear, the prosecution has the burden of proving that you committed the offense alleged in the ticket.
Perhaps the closest example there is to a presumption of guilt (either rebuttable or conclusive, depending upon the statute and facts) is a statutory rape law, which in theory, presumes that someone under a certain age does not have the capacity to consent to intercourse, rendering the offense rape. But, a more straightforward way of understanding those laws is that sex with a minor in the circumstances described is itself illegal without regard to any conclusive presumption of lack of consent.
There are also many laws prohibiting certain people from testifying about certain matters in certain circumstances.
For example, spouses may not testify against each other in court over a spouse's objection in many kinds of cases. These rights are called "privileges" and are not considered to be titles of nobility.
The U.S. Code of Military Justice, intentionally allocates legal rights in these quasi-criminal proceedings in a manner that treats people with different military ranks unequally. Officers have different legal rights than enlisted soldiers, for example. But, since military offices are not hereditary, these rights are not titles of nobility.
