As @mins indicated there are retrofit LCD displays available for the B737 Classic.
The 737NG series aircraft were initially certificated with CRT displays. As CRT technology became obsolescent and very quickly non-procurable in the late 1990's Boeing needed to address the issue for both existing aircraft and future production.
Rockwell Collins was the B737NG display system supplier and developed an LCD Display Unit (DU) to replace the earlier CRT DU. These became the standard production DUs about 1999 (less than two years after the NG's entry into service). As they were certificated in the aircraft, they were also available to replace the CRT DUs in earlier production aircraft.
There were concerns by the FAA at the time about mixing DU types on the flight deck. The solution was to replace all DUs with LCD DUs if one of the CRT DUs failed and there was no spare CRT DUs available.
A similar issue existed for the B747-400. Due the the different economy of scale, they made the effort to certificate the use of mixed display types. That was around 2001.
By 2002, the 737 Aircraft Maintenance Manual makes no reference to the CRT displays:
The display unit (DU) is a flat panel liquid crystal display (LCD)
unit. The LCD makes a high resolution color image of the flight data.