EDIT: I have apparently skipped the domain in which you wish to use the expression. In technical context, development is 开发 not 发展, the latter is economic or similar. So the expression is 开发与支援.
Use another conjuction that is more appropriate for formal written language: 与.
The phrase you are looking for is: 发展与支援. With double quotes (") this gives ~24.6k search results on Google.
Actually the 和 variant gives more results than the one I have quoted, but for the name of an institution, book title, or other formal usage 与 is more appropriate. In spoken language your version is OK, too. The translations for 'development' and 'support' are correct.