How about a one-liner with a list comprehension? Technically its 93 characters long, spare me PEP-8 purism. The regex.findall answer is the most readable if its a high level piece of code. If you're building something low level and don't want dependencies, this one is pretty lean and mean. I'm giving the overlapping answer. Obviously just use count like the highest score answer if there isn't overlap.
def count_substring(string, sub_string):
return len([i for i in range(len(string)) if string[i:i+len(sub_string)] == sub_string])