How to set 19.5Hz PWM frequency?

1000000 / 19.5 = 51282.0512821 microseconds. Let's call it 51282. I doubt the extra precision is going to matter with a solenoid.

This might work...

const uint8_t SOLENOID_PIN = 13;

const unsigned long PulseWidth = 51282UL;

static unsigned long PreviousLeadingEdge;
static unsigned long CurrentHighWidth;

void setup( void 0
{
  pinMode( SOLENOID_PIN, OUTPUT );
  CurrentHighWidth = (PulseWidth / 2) /* some fraction of PulseWidth */;
}

void loop( void )
{
  unsigned long Now;

  Now = micros();

  if ( Now - PreviousLeadingEdge >= PulseWidth )
  {
    digitalWrite( SOLENOID_PIN, HIGH );
    PreviousLeadingEdge += PulseWidth;
  }

  if ( Now - PreviousLeadingEdge >= CurrentHighWidth )
  {
    digitalWrite( SOLENOID_PIN, LOW );
  }
}