In [1]: import numpy as np

In [2]: a = np.array([[1, 2, 3], [4, 5, 6]])

In [3]: b = np.array([[9, 8, 7], [6, 5, 4]])

In [4]: np.concatenate((a, b))
Out[4]: 
array([[1, 2, 3],
       [4, 5, 6],
       [9, 8, 7],
       [6, 5, 4]])

or this:

In [1]: a = np.array([1, 2, 3])

In [2]: b = np.array([4, 5, 6])

In [3]: np.vstack((a, b))
Out[3]: 
array([[1, 2, 3],
       [4, 5, 6]])

The problem that stack functions don't work, is that they need that the row added is of the same size of the already present rows. Using np.array([[]]), the first row is has a length of zero, which means that you can only add rows that also have length zero.

In order to solve this, we need to tell Numpy that the first row is of size two and not zero. The array thus needs to be of size (0, 2) and not (0, 0). This can be done using one of the array-initializing functions that accept size arguments, like empty, zeros or ones. Which function does not matter, as there are no spaces to fill.

Then you can use one of the functions mentioned in comments, like vstack or stack. The code thus becomes:

import numpy as np
all_coordinates = np.zeros((0, 2))

for y in range(2):
    for x in range(2):
        coordinate = np.array([[x,y]])

        # append
        all_coordinates = np.vstack((all_coordinates, coordinate))

print(all_coordinates)

Nest the arrays so that they have more than one axis, and then specify the axis when using append.

import numpy as np
a = np.array([[1, 2]]) # note the braces
b = np.array([[3, 4]])
c = np.array([[5, 6]])

d = np.append(a, b, axis=0)
print(d)
# [[1 2]
#  [3 4]]

e = np.append(d, c, axis=0)
print(e)
# [[1 2]
#  [3 4]
#  [5 6]]

Alternately, if you stick with lists, use numpy.vstack:

import numpy as np
a = [1, 2]
b = [3, 4]
c = [5, 6]

d = np.vstack([a, b])
print(d)
# [[1 2]
#  [3 4]]

e = np.vstack([d, c])
print(e)
# [[1 2]
#  [3 4]
#  [5 6]]