Is there any way to export specific models to SQLite in Django?

I need in my project (based on Postresql) to export few models as SQLite dump. It must be made 'on-demand' f.e. on user request.

What is the easiest way to do it?

I can prepare appropriate database manually, but I would like to omit the duplication of information about schema. I dream about solution like 'dumpdata app-name' but instead of JSON/XML/YAML there should be SQLite. Is there such solution?