I ended up writing my own. It can be called like 
URIUtils.withQuery(uri, "param1", "value1", "param2", "value2");
which isn't so bad.
/**
 * Concatenates <code>uri</code> with a query string generated from
 * <code>params</code>.
 *
 * @param uri the base URI
 * @param params a <code>Map</code> of key/value pairs
 * @return a new <code>URI</code>
 */
public static URI withQuery(URI uri, Map<String, String> params) {
    StringBuilder query = new StringBuilder();
    char separator = '?';
    for (Entry<String, String> param : params.entrySet()) {
        query.append(separator);
        separator = '&';
        try {
            query.append(URLEncoder.encode(param.getKey(), "UTF-8"));
            if (!StringUtils.isEmpty(param.getValue())) {
                query.append('=');
                query.append(URLEncoder.encode(param.getValue(), "UTF-8"));
            }
        } catch (UnsupportedEncodingException e) {
            throw new RuntimeException(e);
        }
    }
    return URI.create(uri.toString() + query.toString());
}
/**
 * Concatenates <code>uri</code> with a query string generated from
 * <code>params</code>.  The members of <code>params</code> will be
 * interpreted as {key1, val1, key2, val2}.  Empty values can be given
 * as <code>""</code> or <code>null</code>.
 *
 * @param uri the base URI
 * @param params the key/value pairs in sequence
 * @return a new <code>URI</code>
 */
public static URI withQuery(URI uri, String... params) {
    Map<String, String> map = new LinkedHashMap<String, String>();
    for (int i = 0; i < params.length; i += 2) {
        String key = params[i];
        String val = i + 1 < params.length ? params[i + 1] : "";
        map.put(key, val);
    }
    return withQuery(uri, map);
}