You will have no problem finding an RE in Belfast: one example the 69 Stranmillis route has had several at a time (in all day service) working in the last few weeks. But just go to the City Hall (where all the Citybuses depart from) and you are bound to have a choice. Belfast to Newtownards in the afternoons used to be good for Ulsterbus REs but as somebody said below they are all gone now. But you can still get Leopards to Newtownards (from Laganside bus station) in the afternoons and it is a nice route, taking you out past Stormont etc. If you take one that is marked as 'via New Road' or 'via Dual Carriageway' in the timetable you will get a run on a short stretch of dual carriageway near Newtownards, which is good fun.One route that I can almost guarantee to be Leopard operated is the 17:00 from Ballynahinch to Belfast (Europa Bus Station) and corresponding 18:00 from Belfast to Drumaness. You could get it out as far as Carryduff and then come back in if you didn't want to go to Ballynahinch.
I'm sure some afternoon Ulsterbus routes from Belfast (Laganside) to Comber (rte 11) or Ballygowan (rte 12) could also be guaranteed to be operated by Leopards (because they are on sub-depot duties) but I don't know which ones; maybe somebody could help. If you look in the message board archive there was a post about this a long time ago.
I don't think they will vanish in the near future, certainly not the Leopards anyway as there are now some 23-year-old Leopards still in service and it will take a long time to replace them all. RE withdrawal is prioritised over Leopards as spare parts for them are more scarce.
Now is a good time of year as several withdrawn REs and Leopards have been re-instated recently but I don't think there any more new bus orders in the pipeline so the fleet might stay steady for the next year.