Bilateral Agencies are aid agencies funded by developed countries to support both governments and the civil society in developing countries. You should conduct preliminary research to understand which agencies are working in your geographical area, what programmes they run, and how to contact them. In fact, majority of these funds are administered directly by embassies and consulates, which act as the first contact point for civil society members. Among main bilateral agencies there are:
1) USAID supports organisations promoting economic growth, improving health and education standards, and working to implement democratic reforms in developing countries. USAID publishes its calls for proposals through grant.gov and Fedbizops.gov. You should constantly monitor these websites to find granting opportunities. The grant making process is well explained in the “respond to a solicitation” at this link.
2) AusAid supports small and medium size NGOs mostly working in Africa, Asia and the Pacific area, although there might be specific funding allocated to respond to emergencies in other parts of the world. NGOs from developing countries could benefit from the Funding to Developing Country NGOs Scheme, which comprises the Direct Aid Program scheme (DAP) and the Small Activities Scheme (SAS). To understand whether you can apply for any of these schemes, you should contact the Australian official representatives in your country. More information about the areas where AusAid works could be found here.
3) The Japan International Cooperation Agency financially assists organisations working in the fields of poverty reduction, governance, and security with a particular focus on developing countries. JICA gives grants also for construction projects such as the reconstruction of infrastructure during and after wars. The organisation does not restrict its activities to a specific geographical area and funds projects in Africa, Asia, Europe, the Middle East, Latin America, and Oceania. For a complete list of the several funding schemes administered by JICA please refer to this webpage.
Said that, the best way to know whether your organisation is eligible to any of the available funding is to contact your nearest Japanese official representative.