I can't see anywhere that's doing 1 weeks parking for under £31.99 in April. That's steep.
Cheapest option: Park somewhere like Campbell Road, a nice residential street just outside the parking zones so it's free. Then catch the 100 bus to the airport from opposite Roseburn Terrace (also free, but v. close to Murrayfield stadium and questionnable at night if you chose to park there). It will be about 15-20 mins on the bus from there and £6 return.
http://www.flybybus.com/departures.htmlDefinitely not got the safety/convenience factor of the airport parking, but there's nowhere near the airport to securely park on the cheap. If you're parking 3 times in April, that's about £100 - I pay that for a 1 year street parking permit in Edinburgh.
If you do lean towards the airport parking, I'd recommend
http://www.secureairparks.com/. It's a 2 min bus ride from the airport, cheapest place will be about 10-15 mins which defeats the purpose. I've used them myself, too.