See this page for more details about the Configsets API:
https://solr.apache.org/guide/solr/latest/configuration-guide/configsets-api.html

• HTTP Request (URL):
  ► V1 API:
  http://localhost:8983/solr/admin/configs?action=List&omitHeader=true&wt=xml&indent=true
  
  ► V2 API:
  http://localhost:8983/api/cluster/configs?omitHeader=true&wt=xml&indent=true
  
  These parameters can be added to the request:
  
  • omitHeader=true
    
    
  • wt=json
    
    
  • indent=true
    
  
  
• Java sample:
  

  private void listConfigSets(final int jettyPort) throws IOException {
      final String url = "http://localhost:"
              + jettyPort
              + "/solr/admin/configs?action=LIST";
  
      final HttpGet request = new HttpGet(url);
  
      try (final CloseableHttpClient client = HttpClientBuilder.create().build();
              final CloseableHttpResponse response = client.execute(request)) {
          final HttpEntity entity = response.getEntity();
  
          System.out.println(IOUtils.toString(entity.getContent(), "UTF-8"));
  
          // close the content stream.
          EntityUtils.consumeQuietly(entity);
      }
  }

To upload a Configset, you need to prepare the zip file that has to be created from within a directory where the solr configuration files ("solrconfig.xml", ...) are directly located. Solr configuration files must be the top level entry in the zip file.

Create the zip file:

$ (cd /opt/solr/server/solr/configsets/_default/conf && zip -r - *) > /opt/solr/_defaultUploadedConfigSet.zip

Upload the zip file and create a Configset:

$ curl -X POST \
--header "Content-Type:application/octet-stream" \
--data-binary @/opt/solr/_defaultUploadedConfigSet.zip \
"http://localhost:8983/solr/admin/configs?action=UPLOAD&name=_defaultUploadedConfigSet"

You can use this command if you want to create and upload the zip file and create the Configset at the same time:

$ (cd /opt/solr/server/solr/configsets/_default/conf && zip -r - *) | curl -X POST \
--header "Content-Type:application/octet-stream" \
--data-binary @- \
"http://localhost:8983/solr/admin/configs?action=UPLOAD&name=_defaultUploadedConfigSet1"

Create a new Configset ("configSetName") based on an existing Configset ("baseConfigSetName").

The Configset can be created as immutable ("configSetProp.immutable=true"), which means it cannot be edited or deleted and its Schema cannot be updated by the Schema API.

• HTTP Request (URL):
  ► V1 API:
  http://localhost:8983/solr/admin/configs?action=CREATE&name=_default1&baseConfigSet=_default&configSetProp.immutable=false
  
  ► V2 API:
  

  $ curl -X POST -H 'Content-type: application/json' \
  -d '{
    "create":{
      "name": "_default2",
      "baseConfigSet": "_default"
    }
  }' \
  http://localhost:8983/api/cluster/configs?configSetProp.immutable=false

  
  
• Java sample:
  

  private void createConfigSet(final int jettyPort, final String configSetName, final String baseConfigSetName) throws IOException {
      final String url = "http://localhost:"
              + jettyPort
              + "/solr/admin/configs?action=CREATE"
              + "&name=" + configSetName
              + "&baseConfigSet=" + baseConfigSetName
              + "&configSetProp.immutable=false";
  
      final HttpGet request = new HttpGet(url);
  
      try (final CloseableHttpClient client = HttpClientBuilder.create().build();
              final CloseableHttpResponse response = client.execute(request)) {
          final HttpEntity entity = response.getEntity();
  
          System.out.println(IOUtils.toString(entity.getContent(), "UTF-8"));
  
          // close the content stream.
          EntityUtils.consumeQuietly(entity);
      }
  }

You will get an error if you try to delete a Configset that is used by collections.
You have to delete those collections to be able to delete the Configset.

• HTTP Request (URL):
  ► V1 API:
  http://localhost:8983/solr/admin/configs?action=DELETE&name=_default1
  
  ► V2 API:
  

  $ curl -X DELETE http://localhost:8983/api/cluster/configs/_default2

  
  
• Java sample:
  

  private void deleteConfigSet(final int jettyPort, final String configSetName) throws IOException {
      final String url = "http://localhost:"
              + jettyPort
              + "/solr/admin/configs?action=DELETE"
              + "&name=" + configSetName;
  
      final HttpGet request = new HttpGet(url);
  
      try (final CloseableHttpClient client = HttpClientBuilder.create().build();
              final CloseableHttpResponse response = client.execute(request)) {
          final HttpEntity entity = response.getEntity();
  
          System.out.println(IOUtils.toString(entity.getContent(), "UTF-8"));
  
          // close the content stream.
          EntityUtils.consumeQuietly(entity);
      }
  }