Websites for a Non Profit Organisation

If you based in South Africa you can use this organisation which offers websites at a low cost.

http://www.phambano.org.za/portfolio/

If you outside of South Africa, look for organisations that assist other organisations im building online presences.

Also, look out for opportunities to have it done at a hackathon. It is a meeting of software development teams who work together say over a weekend on project. Sometimes these events are non profit organisations.

Finally, you could try Wix or something similar.