He'll give you Lorazepam but won't switch you to Diazepam instead if you tell him/her that you no longer wish to take benzo's and want to taper off?? I find that strange but I'm sure you will tell me why!
Firstly, great that you only take 2mg twice daily, thats not a huge dose by anyone's standards, and it will be a lot easier for you to stop than say someone using 8mg daily.
How long have you been taking this medication? I assume this is prescribed by your Dr? ( if not I can understand why you won't get Diazepam.. )
I'd say an
easy and comfortable taper would be something like this:
Take 1.75mg twice daily for a week
Take 1.5mg twice daily for a week
Take 1.25mg twice daily for a week
Take 1mg twice daily for a week
Take 0.75mg twice daily for a week
Take 0.5mg twice daily for a week
Take 0.5mg once a day ( waiting as long as possible in the day before dosing )
Take 0.4mg once a day
Take 0.3mg once a day
Take 0.2mg once a day
If you actually get to this point it would be pretty safe to stop completely, and you would have done it without any nasty nasty withdrawals.
I'm sure someone will give you further advice if needed/requested/warranted if my advice is 'faulty'
Good Luck Man.