Literature shows such a laser is possible with a laser tube 40cm long made of 1mm i.d. glass capillary. Pressures are low and should be between 0.2 to 0.4 torr for the 594nm orange and 614nm red lines. As well, these lines appear only in a pure discharge so a decent vacuum system is required. Looks relatively easy to make it work otherwise. If a laser dye is added to, say, acrylic resin and cast in the form of a rod, a nitrogen-laser pump might be able to make it lase.
Faster discharges mean lower threshold energies as well.
A simple homebuilt capacitor and flashlamp operating at low capacitances but high voltages should discharge in 100nS or less and allow a low-threshold laser to work. One could then do a parametric study of the laser pump. In a similar vein to the above, a superradiant dye laser. This has been demonstrated by using a capillary or a slab and fast flashlamp discharge. If the laser is brought just under the superradiant lasing threshold it may be used as a 'normal' dye laser.