Write a function `count_list_occurrences` that takes a list of lists as input and returns a dictionary. Each key in the dictionary should be a tuple representation of a sublist, and the corresponding value should be the count of how many times that sublist appears in the input list.
#### Example Usage
```python [main.nopy]
count_list_occurrences([[1, 2], [3, 4], [1, 2], [5, 6]])
# Output: {(1, 2): 2, (3, 4): 1, (5, 6): 1}
count_list_occurrences([['a', 'b'], ['c'], ['a', 'b'], ['a', 'b']])
# Output: {('a', 'b'): 3, ('c',): 1}
```