I get the following error when trying to import gtk in Python 2.7 :
>>> import gtk
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "gtk/__init__.py", line 40, in <module>
    from gtk import _gtk
  File "/usr/lib/python2.7/site-packages/cairo/__init__.py", line 1, in <module>
    from ._cairo import *  # noqa: F401,F403
ImportError: /usr/lib/python2.7/site-packages/cairo/_cairo.so: undefined symbol: cairo_tee_surface_index
And I get the following error when trying to import cairo from Python 3.6:
>>> import cairo
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/usr/lib/python3.6/site-packages/cairo/__init__.py", line 1, in <module>
    from ._cairo import *  # noqa: F401,F403
ImportError: /usr/lib/python3.6/site-packages/cairo/_cairo.cpython-36m-x86_64-linux-gnu.so: undefined symbol: cairo_tee_surface_index

I compiled and built the modules in the order as given in the BLFS book.
I also installed cairo as given in the book with tee enabled.
My system is an LFS, with 4.14.4 Kernel Version, with Python 2.7.14 and Python 3.6.4.
EDIT: Downloaded the source and did 'make uninstall' and then reinstalled it. Now I can import cairo without any errors.
I just shifted on older version of pycairo.  Try downloading version 1.11.0.
pip uninstall pycairo pip install pycairo==1.11.0
You can do shift on other versions available too.
At this time; they are:-
1.11.0, 1.11.1, 1.12.0, 1.13.0, 1.13.1, 1.13.2, 1.13.3, 1.13.4, 1.14.0, 1.14.1, 1.15.0, 1.15.1, 1.15.2, 1.15.3, 1.15.4, 1.15.5, 1.15.6, 1.16.0, 1.16.1, 1.16.2, 1.16.3, 1.17.0, 1.17.1, 1.18.0
I don't know much about its internals, i just used brute force to get a solution.
Hope it helps.
Python : Import cairo error (2.7 & 3.6) undefined symbol: cairo_tee_surface_index