You can call the CEE3DLY service in 24- 31- or 64- bit mode to delay a task to the nearest second. It is CICS save and will only delay the thread.
An example:
IDENTIFICATION DIVISION.
PROGRAM-ID. SLEEPYTM.
ENVIRONMENT DIVISION.
DATA DIVISION.
WORKING-STORAGE SECTION.
01 WAIT-PARM.
05 WAIT-SECS PIC S9(8) COMP VALUE 90.
05 WAIT-FC PIC X(12).
PROCEDURE DIVISION.
CALL CEE3DLY USING WAIT-SECS WAIT-FC
GOBACK.
You can see more detail here:
IBM Language Environment Callable Services - Sleep