Java doesn't have such kind of method, but you can check whether a string can be represented properly in a specific character encoding, by trying encoding/decoding.
For example, you can make your own string.canBeConvertedToStringEncoding equivalent as follows:
import java.io.UnsupportedEncodingException;
class Main {
  public static void main(String[] args) throws UnsupportedEncodingException {
    if (canBeConvertedToStringEncoding("abc", "ISO-8859-1")) {
      System.out.println("can be converted");
    } else {
      System.out.println("cannot be converted");
    }
    if (canBeConvertedToStringEncoding("あいう", "ISO-8859-1")) {
      System.out.println("can be converted");
    } else {
      System.out.println("cannot be converted");
    }
  }
  public static boolean canBeConvertedToStringEncoding(String target, String encoding) throws UnsupportedEncodingException {
    String to = new String(target.getBytes(encoding), encoding);
    return target.equals(to);
  }
}