We can use cython 0.27.3 on all versions.

Makefile

@@ -172,7 +172,7 @@ develop:
 # Then start installing our deps so they can be cached. Note that use of --build-options / --global-options / --install-options
 # disables the cache.
 # We need wheel>=0.26 on Python 3.5. See previous revisions.
-	${PYTHON} -m pip install -U -r ci-requirements.txt
+	time ${PYTHON} -m pip install -U -r ci-requirements.txt
 	GEVENTSETUP_EV_VERIFY=3 time ${PYTHON} -m pip install -U -e .
 	ccache -s
 	@${PYTHON} scripts/travis.py fold_end install

ci-requirements.txt

 setuptools
 wheel
-cython>=0.27.3 ; python_version < '3.7'
-# Thread state changes, especially in Pythran seem to need this,
-# which in turn requires CPython 3.7.0a3 or above
-git+https://github.com/cython/cython#egg=cython ; python_version >= '3.7' --install-option="--no-cython-compile"
-# Thread state changes again; requires 0.4.13, as yet unreleased
+# Python 3.7b1 requires at least this version.
+# 0.28 is preferred due to 3.7 specific changes.
+cython>=0.27.3
+# Python 3.7b1 requires this.
 greenlet>=0.4.13
 pylint>=1.8.0
 # pyyaml is included here and doesn't install on travis with 3.7a3
@@ -12,7 +11,7 @@ prospector[with_pyroma] ; python_version < '3.7'
 coverage>=4.0
 coveralls>=1.0
 # See version requirements in setup.py
-cffi
+cffi ; platform_python_implementation == "CPython"
 futures
 dnspython
 idna