There are moves within the UN, and especially the UN Human Rights Council, to develop an international convention against the death penalty. Historically, Quakers have been strongly opposed to the death penalty, and have been involved in advocacy and campaigns to abolish it.
The death penalty convenes two human rights in the UN Declaration of Human Rights (1948): the right to life; and protection from torture.
These recent developments are summarized by the World Coalition Against the Death Penalty,
One of the recent resolutions at the UN Human Rights Council was to condemn use of the death penalty against people for being in same sex relationships. America one of 13 countries on the Human Rights Council to oppose this historic vote. The vote in Geneva passed with 27 of the 47-member Human Rights Council in favour.
There are currently six countries where the death penalty is used for people in same-sex relationships: Iran, Saudi Arabia, Sudan, Yemen, Nigeria and Somalia. This number rises to eight if the Isis-occupied territories of Iraq and Syria are included. There are another five countries where it is technically allowed, but not actually used in reality.
America was one of 13 countries on the Human Rights Council to oppose this historic vote. The US later clarified that this was due to what they felt were wider criticisms against the death penalty, and they do oppose it being applied because of a same sex relationship.
A recent article on this:
Quakers: the Quakers in the World website has a brief summary of Quaker work against the death penalty in the UK, and the wider world. QUNO in New York and Geneva continue this work. http://www.quakersintheworld.org/quakers-in-action/53/Campaigning-against-Capital-Punishment-in-Britain