Lead time is very much a problem here. Also, as an overseas volunteer you, arguably, must be able to add value that a local couldn’t (I remember a guy in the US who spoke German perfectly and that was the reason a colleague thought he should be used in Germany rather than one of the 50,000,000 Germans already there). A sponsoring organization also would have the burden of acquiring your entry visas and work permits, usually, not an easy task in a country where the unemployment rate may be well north of 10%.
If you have skills and credentials, there are a couple of possibilities. Check the IESC (International Executive Service Corps). I don’t recall the URL but they often have overseas Volunteer Vacations opportunities, although they are generally of a longer duration. A source for actual employment that I like is _The Economist_. It publishes many ads from international consulting firms looking for experts for long and short term foreign assignments.