A straightforward line & frame sync generator can be built up with simple logic ICs.
If you also need an input to allow it to lock to an existing video signal, such as for overlaying video or captioning on another image, then it it quite a bit more complex.
The SAA1043 has the option for locking to an external signal.
If you don't need that, the simplest option is a ZNA234E - they are still available on ebay, though not cheap.
Those are actually a pattern generator in a chip, but you can ignore the other outputs and just use the sync signals.
Data:
https://www.mikrocontroller.net/wikifiles/9/9e/ZNA234E.pdf
Ebay: **broken link removed**
Other than that you are looking at built-up circuits or something like a gate array IC programmed to produce the appropriate timing signals.
Or, a PIC or similar MCU, fast enough to produce the timing signals and, with suitable programming, allow locking to external sync if needed.