Very simple to do solo on Nacht der Untoten. There are only 9 weapons spread across the map that you need to buy.
This will be made drastically easier by building up the most points as quickly as possible. The safest & easiest way to do this is to shoot zombies in the chest area with 4-5 bullets from the starting pistol and finish them off with a melee kill - this gives you the most points per kill. Do this until you run out of ammo. Next you can simply move into each area and buy the next weapon as you can afford it.
1. Kar98k & M1A1 Carbine are in the starting room
2. Go through the "Help!" door to buy the Thompson & Double-Barrelled Shotgun
3. Upstairs is the BAR, M1897 Trench Gun, Sawed-Off Double-Barrelled Shotgun, & Stielhandgranates (Grenades)
4. Also upstairs inside the cabinet near the fire is the Scoped Kar98k
If you have any trouble then you can always change the order in which you buy the weapons. The Trench Gun & Thompson are particularly useful so you could open one of the areas earlier to focus on buying one of those.