Hi Frank
I know how you feel. The original trainer that was to take my girl couldnt as she became very ill shortly before and required extensive hospital treatments. (the trainer that is, not my dog)
There are plenty of greyhound trainers that advertize in the papers like The Leader and Recorder. Most of them you have to book in some weeks/months ahead of time, especially if they are regarded as the good ones. My girl was broken in by Anthony Azzopardi in Richmond. I couldnt be happier with the way he treated her. He is Moneyshot Lodge in the Leader. Dont have the number handy.
I dont know any actual trainers that keep the dogs after breaking in so cant help you with that one. The initial beaking in takes about 4 weeks and costs around $300- 350 depending on who does it for you.
I went to the local trial track and asked around for recommendations. It is amazing what you get told about who to use and who to stay well away from, how the dogs are treated etc.
As for actual training I am doing it myself. I wasnt too sure about doing it but spoke to lots of trainers and they all said go and do it yourself. This is my first grey and believe me it is really easy. There are plenty of really nice grey people out there that will give you advice, just get out to the tracks and meet people. Lots of them are willing to help.
I am just waiting for my girl's name to come back and then she is off to the track. No more dog shows which she will be happy about as she is really bored with them. Even though she was RUBIG on the weekend
Good luck and let us know how you go.