I don't have direct experience, but I believe that system/360 programs have historically not had stacks, opting instead for a statically allocated 'program save area'.

https://people.cs.clemson.edu/~mark/subroutines/s360.html

XPLINK, a different linkage convention, also for MVS, does have use a stack-based convention:

https://www.ibm.com/support/knowledgecenter/en/SSLTBW_2.2.0/...