How can I use different certificates on specific connections?

Create an SSLSocket factory yourself, and set it on the HttpsURLConnection before connecting.

...
HttpsURLConnection conn = (HttpsURLConnection)url.openConnection();
conn.setSSLSocketFactory(sslFactory);
conn.setMethod("POST");
...

You'll want to create one SSLSocketFactory and keep it around. Here's a sketch of how to initialize it:

/* Load the keyStore that includes self-signed cert as a "trusted" entry. */
KeyStore keyStore = ... 
TrustManagerFactory tmf = 
  TrustManagerFactory.getInstance(TrustManagerFactory.getDefaultAlgorithm());
tmf.init(keyStore);
SSLContext ctx = SSLContext.getInstance("TLS");
ctx.init(null, tmf.getTrustManagers(), null);
sslFactory = ctx.getSocketFactory();

If you need help creating the key store, please comment.

---

Here's an example of loading the key store:

KeyStore keyStore = KeyStore.getInstance(KeyStore.getDefaultType());
keyStore.load(trustStore, trustStorePassword);
trustStore.close();

To create the key store with a PEM format certificate, you can write your own code using CertificateFactory, or just import it with keytool from the JDK (keytool won't work for a "key entry", but is just fine for a "trusted entry").

keytool -import -file selfsigned.pem -alias server -keystore server.jks

I read through LOTS of places online to solve this thing. This is the code I wrote to make it work:

ByteArrayInputStream derInputStream = new ByteArrayInputStream(app.certificateString.getBytes());
CertificateFactory certificateFactory = CertificateFactory.getInstance("X.509");
X509Certificate cert = (X509Certificate) certificateFactory.generateCertificate(derInputStream);
String alias = "alias";//cert.getSubjectX500Principal().getName();

KeyStore trustStore = KeyStore.getInstance(KeyStore.getDefaultType());
trustStore.load(null);
trustStore.setCertificateEntry(alias, cert);
KeyManagerFactory kmf = KeyManagerFactory.getInstance("SunX509");
kmf.init(trustStore, null);
KeyManager[] keyManagers = kmf.getKeyManagers();

TrustManagerFactory tmf = TrustManagerFactory.getInstance("X509");
tmf.init(trustStore);
TrustManager[] trustManagers = tmf.getTrustManagers();

SSLContext sslContext = SSLContext.getInstance("TLS");
sslContext.init(keyManagers, trustManagers, null);
URL url = new URL(someURL);
conn = (HttpsURLConnection) url.openConnection();
conn.setSSLSocketFactory(sslContext.getSocketFactory());

app.certificateString is a String that contains the Certificate, for example:

static public String certificateString=
        "-----BEGIN CERTIFICATE-----\n" +
        "MIIGQTCCBSmgAwIBAgIHBcg1dAivUzANBgkqhkiG9w0BAQsFADCBjDELMAkGA1UE" +
        "BhMCSUwxFjAUBgNVBAoTDVN0YXJ0Q29tIEx0ZC4xKzApBgNVBAsTIlNlY3VyZSBE" +
        ... a bunch of characters...
        "5126sfeEJMRV4Fl2E5W1gDHoOd6V==\n" +
        "-----END CERTIFICATE-----";

I have tested that you can put any characters in the certificate string, if it is self signed, as long as you keep the exact structure above. I obtained the certificate string with my laptop's Terminal command line.