from matplotlib import pyplot as plt

fig, ax = plt.subplots()
x=1

def annotate():
    global x
    if x==1:
        x=-1
    else:
        x=1
    ax.annotate(x, (0.5,0.5), textcoords='data', size=10)
    ax.annotate('Other annotation', (0.5,0.4), textcoords='data', size=10)

def onclick(event):
    annotate()
    fig.canvas.draw()

cid = fig.canvas.mpl_connect('button_press_event',onclick)

from matplotlib import pyplot as plt

fig, ax = plt.subplots()
x=1
annotation = ax.annotate('', (0.5,0.5), textcoords='data', size=10) # empty annotate object
other_annotation = ax.annotate('Other annotation', (0.5,0.4), textcoords='data', size=10) # other annotate

def annotate():
    global x
    if x==1:
        x=-1
    else:
        x=1
    annotation.set_text(x)


def onclick(event):
    annotate()
    fig.canvas.draw()

cid = fig.canvas.mpl_connect('button_press_event',onclick)
plt.show()