Firstly again tyshepp, you're misinformed. This is not about homosexual rights. So I'm not exactly sure what your point is or why this is such an important issue for you. This is about the right to privacy for all adults participating in consensual sex in the privacy of their own homes within Belize.
With respect to your specific question, yes, there are international conventions on human rights that cover sexuality. Under the UN, these include:
International Covenant on Civil and Political Rights (1966) (article 2, 26)
Convention on the Rights of the Child (1989) (article 2)
Convention on the Elimination of All Forms of Discrimination against Women
United Nations High Commissioner for Refugees -Since April 1993 the United Nations High Commissioner for Refugees (UNHCR) has recognized in several Advisory Opinions that gays and lesbians qualify as members of a "particular social group" for the purposes of the 1951 Convention and the 1967 Protocol Relating to the Status of Refugees. In its publication "Protecting Refugees," the UNHCR states: "Homosexuals may be eligible for refugee status on the basis of persecution because of their membership of a particular social group. It is the policy of the UNHCR that persons facing attack, inhuman treatment, or serious discrimination because of their homosexuality, and whose governments are unable or unwilling to protect them, should be recognized as refugees." (UNHCR/PI/Q&A-UK1.PM5/Feb. 1996)
Under the ORGANIZATION OF AMERICAN STATES (OAS)
The first case on human rights and sexual orientation in the Inter-American system is that of Marta Alvarez who brought a petition against Columbia before the Inter-American Commission on Human Rights (Velasquez Rodriguez v Honduras, 1998). She was denied the right to equal treatment through the refusal of Colombian prison authorities to grant her the conjugal visits with her partner because of her sexual identity as a lesbian. Colombian law states that conjugal visits are a right for all its citizens, without regard to sexual orientation.
Organization for Security and Cooperation in Europe (OSCE)
The Organization for Security and Co-operation in Europe (OSCE) is the largest regional security organization in the world with 55 participating States from Europe, Central Asia and North America. OSCE was created by the 1975 Helsinki Final Act which contained a provision to "respect … human rights and fundamental freedoms, including freedom of thought, conscience and religion, and belief", as well as "equal rights and self-determination of peoples".
The Parliamentary Assembly of the OSCE passed a declaration in Ottawa in 1995 calling on member states to provide equal protection against discrimination for all, sexual orientation being among the grounds specifically protected from discrimination.
I'm not sure why you believe that one form of discrimination deserves more attention than another. All forms of oppression and discrimination and abuse deserve equal attention and members of those vulnerable communities all deserve protection, whether they are women, men or children. It seems a bit like saying - 'Why are there all these organisations to help dogs and cats when horses suffer so much abuse?'
All of this aside, the current issue in Belize is a human rights issue affecting all adults, not a homosexual issue. As you seem very interested in this subject though, please let me refer you to some further reading International Council on Human Rights Policy - Sexuality and Human Rights Discussion Paper