I have also offered free freelancing samples to my clients in the past and I think that this is the best way to make a customer realise what you are capable of doing. However, offering free trials is a bit hard when you conduct business online.
Whenever the samples of the job that I've done for another client which is almost exactly the same thing that you want me to do for you is not enough to prove that I am capable of doing the job for you, then I will not be interested in taking up the job by providing a free trial service before you can be convinced that I'm going to do the job.