I've done a bit of searching, but unfortunately it seems that when it comes to spent convictions in NSW, there is only the automatic scheme under the Criminal Records Act. I can't find anything about being able to apply to have a conviction spent that is not automatically covered by the Act.
There's a few things I can think of that might help. The first would be that whenever you need to deal with the subject, prepare beforehand on ways to turn negatives into positives. I'm guessing that this is something that might take a bit of practice to get right. For example, when the subject of the actual offence comes up, be honest and speak freely about it (there's no point lying if they already know and being open and honest is always a good thing anyway), but then shift the focus to how you've turned your life around and particularly, the good life that you've now made for yourself and the solid work history that you have under your belt.
If you get the opportunity, I would also try asking questions yourself to make the other party consider their own mistakes. For example, "Do you mind if I ask you a personal question? Have you ever made mistakes?" Any normal person will have to answer yes, at which time you ask "do you think that making those mistakes has made you a better person because of what you learned?" This gives them something to think about, and you then explain that while your mistake may be a lot more serious than many (and you openly recognise this), what you have learned is proportional, and that whole experience has played a big part in making you who you are today - someone with a lot of drive and a desire to succeed and provide a better life for their family etc. The message that you want to get across is that you don't define yourself by your mistakes, but by what you learned from those mistakes and how you implemented that knowledge and moved forward in a positive direction. So it's how you define yourself and who you are today that matters. Showing others how you see youself is the best way to convince them to see you in the same light.
I hope I explained that clearly enough so that you get an idea of what I'm thinking. Basically, get them thinking about themselves a little and then show them that while most peoples instincts may be to focus on the negatives, you are solely driven by all the positives in your life and your desire to keep moving forward onto better things.
If you work for a company that has HR people, they might be able to provide you with tips on how to best handle the subject. If your employer knows about the conviction, then don't forget to convince anyone you talk to that you're just asking for future reference and that you're not about to jump ship. If they don't know, then you can make things a bit easier by simply explaining that you promised a family member or friend that you would try to get some tips to help them out. The point being, that HR people would probably be the best source of what will or won't work at an interview, so the more tips you can get from them on how to deal with the subject, the better.
Other tips I can think of would be that if you are in an industry where many jobs come about by word of mouth, then a good reference from someone already in the company could result in no checks being done even if they normally do them. So if that's the case, always keep your ears open for opportunities.
Another thing is the type of work. If you're interested in driving for example, most jobs would only require that you obtain a copy of your driving record from RMS and don't involve a criminal history check at all. That's just an example, but you get the idea. Criminal history checks cost money, so while many employers do them anyway, the vast majority don't unless they are required to. The good news is that the number of industries where a check is mandatory are minimal when compared to those where it's not.
One thing I will say, is avoid employment agencies whenever possible. I may be wrong about this, but it's my understanding that many agencies will conduct checks once they settle on a final interview list. So if they have a large number of applicants, which is usually the case, it's unlikely that you would reach the interview stage if you have a record. So you pretty much want to stick to applying directly to employers whenever you can.
Finally, have you ever considered starting your own business? It's obviously not for everyone, but if you have an idea, the knowledge and the drive, it might be right for you. The great thing here is that having a record doesn't prevent you from doing courses and obtaining the knowledge you need to run your own show. If you ever consider this option, you just need to make sure that your particular history doesn't exclude you from operating in your chosen industry - but that applies whether you're working for yourself or for someone else anyway.
That's about all I can think of off the top of my head. I hope at least some of it may be helpful.