VolleyでCookieを使い回す ref: http://qiita.com/mochico@github/items/20c228a87e000039cd54

MyJsonObject.java

public class MyJsonObjectRequest extends JsonObjectRequest {
    private MyJsonObjectRequest(int method, String url,
            JSONObject jsonRequest, Listener<JSONObject> listener,
            ErrorListener errorListener) {
        super(method, url, jsonRequest, listener, errorListener);
    }

    public MyJsonObjectRequest(String url, JSONObject jsonRequest,
            Listener<JSONObject> listener, ErrorListener errorListener) {
        super(url, jsonRequest, listener, errorListener);
    }

    @Override
    protected Response<JSONObject> parseNetworkResponse(
            NetworkResponse response) {
        Map<String, String> headers = response.headers;
        if (headers.containsKey(Constants.SET_COOKIE)) {
            mContext.getSharedPreferences(PREF_NAME, Context.MODE_PRIVATE)
                    .edit()
                    .putString(PREF_SAVED_COOKIE, headers.get("Set-Cookie"))
                    .commit();
        }
        return super.parseNetworkResponse(response);
    }

    @Override
    public Map<String, String> getHeaders() throws AuthFailureError {
        Map<String, String> customHeaders = super.getHeaders();
        Map<String, String> newHeaders = new HashMap<String, String>();
        newHeaders.putAll(customHeaders);
        String cookieStr = mContext.getSharedPreferences(PREF_NAME,
                    Context.MODE_PRIVATE).getString(PREF_SAVED_COOKIE, "");
        if (cookieStr.length() > 0) {
            newHeaders.put("cookie", cookieStr);
        }
        return newHeaders;  
    }
}