Whilst I rarely use airport parking as the length of my trips tend to make it uneconomical. I do however recommend this firm at Manchester Airport.
One thing that seems to work with them is go through the booking procedure up to but not including payment and then exit.
Within a day or so an e mail then arrives offering the stay at a discount.
The site is not too far away from the airport, its security is excellent and I have never experienced problems with it.