You can easily do this with an advanced label expression.
For example, I've got a label expression that will take 2 fields and label with whichever of the fields is present, or both. You could do something like the following:

Important notes about the code provided:
- Obviously you would have to change the code to use your own field names
- In the Label Expression dialog, you have to switch the parser to Python, or write your own label expression in your chosen language.
- You have to make sure the "Advanced" check box is selected/turned on.
- The provided code will actually create stacked labels (Field_1 on one line and Field_2 on the next line). If you want it to all be on one line separated by a space, you can change the
"\n"
at the end of the 4th line to just be a space in quotes " "
Code provided below so you can copy past instead of re-typing from screen shot:
def FindLabel ( [FIELD_1], [FIELD_2] ):
lbl = ""
if [FIELD_1] <> None:
lbl += str([FIELD_1]) + "\n"
if [FIELD_2] <> None:
lbl += str([FIELD_2])
return lbl
Let me know if I need to clarify anything in it for you.