Mind you I only have 1 bsd install and it's a dragonfly bsd but they told me to report it here to because of shared ports. :)

py27-rainbowstream-1.3.5 depends on py27-requests-2.11.1(${PYTHON_PKGNAMEPREFIX}requests>=2.5.3:www/py-requests), while py27-livestreamer-1.12.2 uses py27-requests1: 1.2.3 (${PYTHON_PKGNAMEPREFIX}requests1>=0:www/py-requests1) This makes it so that you can only install either one or the other, both binary package or from ports.

changing py27-livestreamer-1.12.2 to use the same dependency as the rainbowstream package fixes this issue. Afterwards my limited testing works fine (I only use twitch.tv though) and all unit tests in the original source pass. (tested by me by running 'python -m unittest discover' on '/usr/obj/dports/multimedia/livestreamer/livestreamer-1.12.2/' ) From what I can tell from skimming the source of livestreamer the requests module is only used for simple get calls.

fix for ports:

replace ${PYTHON_PKGNAMEPREFIX}requests1>=0:www/py-requests1 \ 
with ${PYTHON_PKGNAMEPREFIX}requests>=2.5.3:www/py-requests \ 
in /usr/ports/multimedia/livestreamer/Makefile