How to check for an integer or a string and if not ask again [Java]

Consider creating a method for reading in a valid integer. Pass this method the valid integer range. The method would attempt to read the value once and validate. If the method fails, return null, if it passes return the Integer. Call this method in a do-while loop until you get a non-null Integer.

First off, you really shouldn't use exceptions for input validations. Exceptions are for exceptional conditions; things you don't expect to happen. Josh Bloch outlines this specifically in his excellent book Effective Java

As for your code, I would suggest using the hasNextInt() method combined with getting the input as an int and checking for the range you require as you've actually stated in your question.

int d = 0;

while (d < 1 || d > 31)
{
    System.out.print("Enter the day of the month (1-31): ");
    if (userInput.hasNextInt())
    {
        int d = userInput.nextInt();

    }
    else
    {
        String s = userInput.next();
    }

    if(d < 1 || d > 31)
    {
        System.out.print("That day is invalid - ");
    }    

}

It looks like you are using Scanner to get input. (By the way, in Java, it is conventional for variables to start with lower-case letters).

If that's the case, if you attempt to scan an int when there isn't one in the input, an InputMismatchException will be thrown. You avoid this by testing whether this will happen before you try to read the int.

So, think about a loop structure like this:

int d = 0;
while (true) {
  if (/* The input isn't an integer */) {
    /* Tell the user. */
    continue;
  }
  d = input.nextInt();
  if (/* The input is out of range */) {
    /* Tell the user. */
    continue;
  }
  ...
  /* When you've completed all of your tests and everything is okay, break. */
  break;
}

By the way, many months don't have 31 days.

Are you familiar with the behavior of a try-catch statement?

try
{
   //do something that may throw an exception you can handle
}
catch(Exception ex)
{
   //If we enter this block, an exception was thrown from the try block's code

   //If you cannot fully handle the exception, you can rethrow it
   throw ex;
}
finally
{
   //This code ALWAYS executes, unless the program is aborted from outside its scope
}

You can use this inside some other loop, allowing you to define behavior based on whether an exception was thrown. This code is in C#; it is syntactically very close to Java but I'm a little light on Java's libraries so substitute proper class names/method calls as necessary:

int day = 0;
while(true) //we will manually break out of the loop once the user enters a valid value
   {
      try
      {
        //Ask user for input
        string input = Console.ReadLine();
        day = Int32.Parse(input); //this will throw an exception if input is not numeric

        //You can throw your own exception within a try block too
        if (day < 1 || day > 31) throw new Exception("Date not within proper bounds");

        break; //if the parse worked and the value passed the validation, end the loop.
      }
      catch(Exception ex) //You can catch something more specific
      {
        //The parse failed; tell the user that they screwed up, and how
        Console.WriteLine("Invalid entry: " + ex.Message);
        //skip the rest of the loop's code and start a new iteration of the loop
        continue; 
      }
   }

The behavior of this construct is that while the user keeps entering values that cannot be turned into a number between 1 and 31, exceptions will be thrown, caught, and used to perpetuate the loop. As soon as the user enters something you can work with, execution flow will move past this loop to whatever is next.