With a marriage that took place before Loving vs. Virginia I see three possibilities:
- Your parents didn't disclose your mother's heritage (i.e. she could 'pass').
- Your parents married somewhere else (not likely to be South Carolina or Georgia).
- Your parents married after 1967 (or never married).
Since you have a marriage date, let's assume for the moment that it is correct (although it might not be) and rule out #3.
The trouble with finding vital records in general is that while people often live in the same place for a long time, they can get born, married, and die just about anywhere -- especially in the 20th century, with air travel in the mix. (These days, destination weddings are popular, so people marry far from home without having any kind of compelling reason like getting around the law.)
If your parents disclosed your mother's heritage, simply going to South Carolina wouldn't have been any help. See the map which is in Wikipedia's article on Anti-miscegenation laws in the United States. For 1954, they wouldn't have been able to marry anywhere inside the Red Zone unless they concealed your mother's heritage.
So how do you find them? And (more importantly) how do you recognize that you have found them, because there might be other couples with the same names that married on the same day?
The basic principles of family history are to start with what you know, to record the source of that information, to evaluate how good that information might be, and to work outward from what you know in small steps rather than big leaps. You have family members to talk to, which is good. Talk to them and record what they can tell you -- everything they tell you, no matter how small the detail.
Then break down what they say into the separate events and attributes, and assemble a timeline. Write a biographical profile of your parents with everything you know about them and who said so. Some people call these things 'facts' but since you weren't there for a lot of the events and don't have direct knowledge of it, these are all 'someone said so' kind of information. You'll see these facts called "assertions" and the reasoning is to remind us that this is all someone's say-so.
Once you have all the assertions placed on a timeline, in chronological order, you can see what you have and pick out the ones that might be good candidates for more research. Ask yourself if any records might have been created that would mention your parents' marriage, and if so, which agency created them, and which agency or archive might hold them now. You'll have to determine for each case whether the search is likely to be worthwhile, because you may not know in advance whether or not the record is actually your father's or your mother's record, or someone else with the same name. The other problems: many 20th-century records are not online, and access can be limited because of privacy restrictions.
For instance: If your father served while he was married, then your father may have needed to ask permission to get married. Your mother may have been listed as a dependent, and he may have had to submit to the Army some kind of information about when and where they were married. Could you find your parents' wedding date and place in his service records? The records themselves are not online, but since you are immediate family you can request that a copy of his paper records be sent to you. See this article at the National Archives about Online Requests Using eVetRecs. But -- and here's the 'gotcha' -- there is also this page: Special Notice Regarding Service Record Requests which explains what information is sent out when you request the records:
This extract contains copies of all essential documents to certify
entitlement to most rights and benefits associated with military
service, to identify key events in a military career, and to identify
significant events in health care. Personal data pertaining to third
parties is redacted from the file, pursuant to Privacy Act provisions.
The purpose of ordering the records, for most families, is to get documents that will show they are eligible for benefits, and thus the information sent out in response to a records request is appropriate for that purpose. So even if the information you seek is in the file, due to the Privacy Act, they may not be able to send it to you. (If you want to request his military records anyway, see also the pages Other Methods to Obtain Military Service Records, Frequently Requested Records Which Are NOT at the National Personnel Records Center, and the Records Location Table which have more information about which agencies hold records and which records are where.) Ask them what information, if any, will be redacted from the file before it is sent to you. (It is possible that the only way you will be able to see the unredacted file is to view it in person at the NPRC, and that you may need to show proof of your relationship.)
If you have access to any family papers, they also might hold clues to where your parents might have married.
It is helpful to keep a log of all the searches you make, any inquiries you make for records, etc. so you can keep track of the work you've already done. It's also helpful to write out a research plan with the specific tasks you haven't done yet (e.g. searching for a marriage announcement in local newspapers).
if your parents did go out of town to marry because they wanted to marry somewhere they wouldn't have been known, here are some ideas for places to look: