That is an interesting issue.  I've not encountered a public records office in the western states (California, Nevada or Arizona) which don't allow a camera.  This includes court clerk offices, recorded deed offices and county board clerk's offices. 

  I would parse why and how this is not allowed.  Is there an actual statute or code preventing it.  If so, what is the exact code.  Once you have the code, go and read the text of the code, including all other parts of that particular law, above and below it.  Understand it and look for legal loopholes and allowances.  Are press journalists exempt?  If so, it might be worth becoming a member of the news media for the value that it affords (California has one exception in Vital Records {birth, death, marriage] for the media, which allows access and makes it effective for us to access such records in this manner). 

  The State Public Records Act or it's equivalent is another thing to read carefully and understand as it might offer such access. 

  Another route is to analyze fair access laws for the disabled.  Does this provde you or your client with access that is fair and resonable if you are using a camera with a wifi card that is streaming your document image to the client live and online?

  The final route to contemplate is, if it is LEGAL, using a pair of DVR sunglasses to record document images.  They are about $200 and great resources for getting clear images of documents.  Combined with press membership, they form a formidable case for any researcher to be, not only a  public records investigator, but an investigative journalist reporting on issues surrounding public records access, published on their own private or public blog. 

 Something to consider:  press protections for  your business.  It's up-front, fair and reasonable to act as an advocate of public records access and to do so with the protections of the media.