Also, in a civil case, isn’t the burden the “preponderence of evidence”, as opposed to “beyond a reasonable doubt”? In this specific instance, there is no evidence presented in the affirmative for Obama (IMO), because he refuses to provide any.
In a civil case, as you note, the burden is on the plaintiff to prove his case by a preponderence of the evidence. But there has to be a civil trial where evidence is introduced, subjected to cross-examination and admitted to the court, assuming it qualifies as appropriate evidence. For instance, hearsay is not permitted and documents must be authenticated, etc. So far no one has presented any "evidence" in any of these cases because evidence is only evidence after it has been introduced in a courtroom, made subject to cross-examination or stipulation and then "admitted" as evidence by the judge. Obama has not been required by any court to present evidence and none of the plaintiffs in these many cases has presented any evidence either. Just saying something is so is not evidence.
I'm not a lawyer, but if the argument is a Constitutional issue, then there wouldn't be any material evidence required, but rather citations from previous opinions, legal scholars, quotations from the Founders writings, etc. would be sufficient.
If however, the argument that the computer-generated Certificate of Live Birth that he's presented isn't sufficient proof of citizenship, then yes, I would think you'd need evidence. And time, and money. It would probably entail researching the Hawaiian statutes in effect in 1961 relating to issuance of birth certificates, plus any archived publications of the Dept. of Health from that period, caselaw from state and circuit courts relating to citizenship, rulings of the Hawaiian AG, legislative records relating to the relevant laws, archived newspaper reports of birth certificate fraud or system tampering/malfunction, and a possible real-life example of a person whose Hawaiian COLB does not reveal the actual facts of their birth, such as an adoptee, etc.
If the argument is that he was born in Kenya, then I think you'd have to provide some actual evidence to prove it. So far (and this doesn't apply to Donofrio, because his was a Constitutional issue), all I've seen are statements that "it's been said that" or "there are reports of" or I believe in one case, a recording of an African grandmother saying he was born in Kenya in a phone conversation with a third party. (I doubt that O's elderly and illiterate grandmother would qualify as a credible witness, since she's also told quite the opposite story.)
If the argument is that the COLB scan posted on the internet is counterfeit, then wouldn't it make sense to ask the Obama campaign if a qualified document expert could examine the physical document? If they refused, then the refusal itself would be suggestive.