For a lower output frequencey (e.g. up to 100 kHz) a normal potentiometers is OK and also digital potentiometers work (keep in mind the signal has to stay inside the supply range).
The variable gain amplifiers come as integrated circuits and are not common to use with hooby systems like the Arduino - so no such boards. Many of the variable gain amplifers are controlled with a votlage or current.
Variable attenuators / amplifiers for the RF range come as rather expensive modules, so not suitable here.