Being Curious, I managed to find this on Georgia law. Note this is not exclusively about coin hunting, so keep looking :
Is it Legal for Hobbyists to Collect Artifacts or Dig for Artifacts?
Getting a Permit
The Office of the State Archaeologist is authorized under Official Code of GA (OCGA) Section 12-3-52(c) to grant permits to recognized scientific institutions or qualified individuals (professional archaeologists) to conduct archaeology on state properties. Requirements for this work can be found on our website at this link under Research on DNR-Managed Lands: http://www.gashpo.org/content/displaycontent.asp?txtDocument=346
Permits are only granted to professional archaeologists or graduate students in a recognized, university archaeology program. Otherwise, collecting or digging for artifacts is prohibited on state-owned lands.
When Is it Legal for Hobbyists to Collect Artifacts or Dig for Artifacts?
Surface collecting:
1. It is legal to collect artifacts from the surface of dry land on privately owned property if the land is not posted, gated, or fenced against entry. We recommend obtaining written permission from the landowner to protect the property owner's rights and to protect the visitor from trespassing. (OCGA 12-3-621)
2. It is not legal to surface collect, dig, or metal detect on state property. This includes Civil War sites. (OCGA 12-3-10

, [12-3-52)
Digging/Metal Detecting:
1. With the exception of burials and associated objects, archaeological sites belong to the landowner. Landowners can dig archaeological sites - with the exception of burials - that are on their property. DNR recommends that you preserve any archaeological sites that you may own for future generations.
2. On privately-owned land, it is legal to dig for artifacts (including when artifacts have been found by metal detecting) if you have written permission of the landowner. All lands in Georgia are either owned privately or by the local, state, or federal government. This includes Civil War sites.
Hobbyists and professional archaeologists alike must determine who owns the land and ask their permission first, before undertaking any activity.
Further, OCGA 12-3-621 requires any person desiring to dig for artifacts to notify the state archeologist before beginning any such investigation or disturbance, which can be done through this HPD Web page. Click here for email and or call the telephone hot line number, available at all times: 1-866-755-0014.
3. It is not legal to surface collect, dig, or metal detect on state property. This includes Civil War sites. (OCGA 12-3-10

, 12-3-52)
4. It is not legal to disturb or dig human burials or collect human skeletal remains or objects associated with burials, regardless of who owns the land. Three Georgia laws prohibit disturbing graves: OCGA 31-21-44, 31-21-6 and 36-72-1 through 16. If human remains are inadvertently discovered, STOP all land disturbing activity immediately, protect the burial from harm, and notify the local law enforcement authority. As required under OCGA 31-21-6, law enforcement officials will then notify the coroner, the local government, and the Georgia Department of Natural Resources, who will recommend a permanent protection plan.
In the Water or On the Beach:
1. It is legal to collect artifacts with the permission of the landowner in privately-owned waterways.
2. It is not legal to take artifacts off the bottom of state-owned waters. (OCGA 12-3-80).
3. If the body of water you're interested in is owned or managed by a local or federal government agency, contact that agency for their policy on artifact collecting.
4. To collect artifacts or metal detect on beaches along the coast of Georgia, it is also necessary to first determine ownership of that land and ask permission. Beaches may be private or owned by a governmental agency. To determine who the landowner is, you might start by contacting the DNR Law Enforcement Region VII Office in Brunswick, telephone: (912) 264.7237, address: Suite 201, One Conservation Way, Brunswick, GA 31520.
For a detailed description of the laws as they apply to Georgia's waters, follow this link http://www.gashpo.org/content/displaycontent.asp?txtDocument=153