You're going to have create your own mapping.
Here's what already exists: Joda Time has a method DateTimeFormat.patternForStyle, which delegates to the patterns specified by the JDK in java.text.DateFormat. See Using Predefined Formats, which provides the following table:
Style       U.S. Locale             French Locale
DEFAULT     Jun 30, 2009            30 juin 2009
SHORT       6/30/09                 30/06/09
MEDIUM      Jun 30, 2009            30 juin 2009
LONG        June 30, 2009           30 juin 2009
FULL        Tuesday, June 30, 2009  mardi 30 juin 2009
You specify which Locale specific format you in patternForStyle by using S, M, L, F, and - to leave it blank. So, in your case, it sounds like you want date only, so use:
DateTimeFormat.patternForStyle("S-", locale);
Unfortunately, this option will result in a TWO digit year.
So, either do all of that, or **create your own map` of DateTimeFormatters for this purpose. Something like:
public class DateFormatterProvider {
  private final Map<Locale, DateTimeFormatter> formatterMap = new HashMap<>();
  public DateFormatterProvider() {
    formatterMap.put(Locale.US, DateTimeFormat.forPattern("dd/MM/yyyy"));
    formatterMap.put(Locale.FRENCH, DateTimeFormat.forPattern("MM/dd/yyyy"));
    // etc.
  }
}