Here's the easiest nobles to get from where I think we are (based on the nobles we had and the nobles we seem to have gotten):
House Ferite Representative: Have 10 trappers, 50 tamed animals, or carry out 10 taming jobs.
-I assume letting the tamed animal population grow will fulfil this. Alternatively trap some elephants and tame them.
The Alchemist
-To get the alchemist, you need to carry out 10 extract or soapmaking jobs. Soap means you slaughter some animals to make tallow, and make an alchemist's workshop. You will need 1-3 logs of wood to make the pearlash for the glass vials, and a further 10 logs of wood to make the lye for the soap. Sand can be obtained from the banks of the cave river.
The House Berite Representative: Have ten farmers or fisherdwarves or complete 450 farming jobs. I think this may well have been done.
The Governor: Have 80 Dwarves and perform diverse tasks. We may have hit this already.
The Order of the Crossbow: We need to produce 50 crossbows to get this. Just put in an order for a lot of crossbows. You can make them out of wood but I think it would be better to make them out of bone.
The Order of the Sword: We can get 50 logs of wood and use 50 boulders of obsidian to produce 50 rock swords, assuming they are considered to be swords.
Treasurer, Hoardmaster, and Dungeonmaster: Make up to 50,000 coins. Each coin job produces 500 coins so we would need up to 100 bars of metal to get this many. However, if the "no economy hack" is around you can probably use the "melting coins generates metal" feature so the use of metal isn't so bad. The trouble with this is it will attract the Baron (but you will already have the Baron if you have the Broker, Manager, and Bookkeeper).
@Currency: I strongly suggest maintaining currency from each year of the fortress so we can see what crazy designs we get.
@Diverse tasks I think given the multiple operational superweapon constructions on the map, we have performed diverse tasks.