Unless you consider the constitution to be the mechanism, which I do. And citizens have 1000% standing to sue to ensure their constitutional rights are upheld.
Are you assuming that there is actually some law regarding the required prood of eligibility of candidates? There may be, but I am not aware of it and no one has referenced it in the many discussions of this.
The Constitution does not say anything about a priori qualification only that one must be a Natural born citizen living here at least 14 yrs. and 35 yrs. of age in order to SERVE. Presumably those who certify the electors in each state would certify that they voted for a qualified candidate.
At the time Cheney receives and counts the votes Congress can object.
Other than State certifications and Congressional acceptance I see no constitutional role for the Court.
Remember the comments from the Founders that this system was set up for Honorable men. It does not work without them. It appears that this is a coupe attempt and Obama is willingly inviting a Constitutional crisis.