It seems as if a digital thermometer with K-Type thermocouples should do the trick. I don't use liquid nitrogen or have a need to measure this low of temperature so I am not answering with first hand experience, but you should be able to find a used Fluke thermometer with K-Type wires on Ebay for not too much cash.
Here's what a quick internet search found:
Type K Thermocouple (Nickel-Chromium / Nickel-Alumel): The type K is the most common type of thermocouple. Its inexpensive, accurate, reliable, and has a wide temperature range. The type K is commonly found in nuclear applications because of its relative radiation hardness. Maximum continuous temperature is around 1,100C.
Type K Temperature Range:
Type K Thermocouple Grade WireThermocouple grade wire, 454 to 2,300F (270 to 1260C)
Type K Accuracy (whichever is greater):
Standard: +/- 2.2C or +/- .75%
Special Limits of Error: +/- 1.1C or 0.4%
Good luck,
Mike L.