Don't bother with The Trainline.com. No online agency can offer fares any cheaper than those on the National Rail website:
http://www.nationalrail.co.uk/
Further you might have to pay booking fees and, even worse, you might end up with tickets which aren't valid for travel on any trains at all. (I used to run a railway station and we frequently encountered travellers who'd purchased 'duff' tickets from online sites. My former colleagues tell me that they still wish that all of the independent online booking sites could be shut down; they don't offer customers anything extra but their errors lead to a lot of stress and hassle for both passengers and rail staff).
The only airline flying between Birmingham and Edinburgh is FlyBe, so I assume that you've already checked their website.
If you're not prepared to consider coach travel I can see no other options.
Chris