I don't know anything about the barometer itself, but I do know a little about the SPI bus. Try this.
pinMode(chipSelectPin, OUTPUT);
// disable SD while read/write to barometer.
// Once SD.begin() runs, this will be HIGH if not in a SD function
pinMode(SD_chipSelectPin,OUTPUT);
digitalWrite(SD_chipSelectPin,HIGH);
//Configure SCP1000 for low noise configuration:
writeRegister(0x02, 0x2D);
writeRegister(0x01, 0x03);
writeRegister(0x03, 0x02);
// give the sensor time to set up:
delay(100);
You may need to check if the barometer library writeRegister (and readRegister?) functions manipulate the SS pin for the barometer. The read/write functions should set the barometer SS LOW, do the read/write, then set the SS pin HIGH.
edit: My bad. I used the wrong SS pin, It should have been SD_chipSelectPin. Also if the barometer read/write routines do not manipulate the SS pin, it isn't hard. Like this:
digitalWrite(chipSelectPin,LOW);
writeRegister(0x02, 0x2D);
writeRegister(0x01, 0x03);
writeRegister(0x03, 0x02);
digitalWrite(chipSelectPin,HIGH);