Jobslinger.com lists more than a dozen that were posted in Alabama yesterday and lists about 400 overall. Most of those will be taken already, but yes, Alabama is shopped. The state is pretty large, so you need to look at that area where you would be willing to drive and search an area like that.
Jobslinger.com is a free signup and even though most of the jobs are taken already, you will be able to see what companies have advertised jobs in your area in the past few months and sign up with them. Generally if a company is shopping a client, they will be shopping that client monthly or quarterly all year.