Android Central Keystore

This is not supported, may break in future versions, etc., but here's how to get a list of the trusted certificates. You cannot add new ones without root access, because /system is mounted read-only. But if you do have root access, you can use the regular KeyStore API's to add certificates.

KeyStore ks = KeyStore.getInstance("BKS");
InputStream is = new FileInputStream("/etc/security/cacerts.bks");
ks.load(is, "changeit".toCharArray());

List<X509Certificate> certs = new ArrayList<X509Certificate>();
Enumeration<String> aliases = ks.aliases();
while (aliases.hasMoreElements()) {
  String alias = aliases.nextElement();
  X509Certificate cert = (X509Certificate) ks.getCertificate(alias);
  certs.add(cert);
}

EDIT: This should work with needing to hardcode the path to the keystore:

TrustManagerFactory tmf = TrustManagerFactory
                    .getInstance(TrustManagerFactory.getDefaultAlgorithm());
tmf.init((KeyStore) null);
X509TrustManager xtm = (X509TrustManager) tmf.getTrustManagers()[0];
for (X509Certificate cert : xtm.getAcceptedIssuers()) {
    String certStr = "S:" + cert.getSubjectDN().getName() + "\nI:"
                        + cert.getIssuerDN().getName();
    Log.d(TAG, certStr);
}

ICS (Android 4.0 / API 14) introduced the TrustedCertificateStore (not directly available in the SDK) that enables you to do exactly that. You can access it using the JCA Keystore api like this:

/**
 * Android Central Keystore repo usually located on /data/misc/keychain 
 * including the system trusted anchors located on /system/etc/security
 */
KeyStore keyStore = KetStore.getInstance("AndroidCAStore");
keyStore.load(null, null); //Load default system keystore
Enumeration<String> keyAliases = keyStore.aliases();

while(keyAliases.hasMoreElements()){
    String alias = keyAliases.nextElement();
    X509Certificate cert = (X509Certificate) keyStore.getCertificate(alias);

    //<User cert in whatever way you want>
}