It appears that at least some pre-IEEE 754 computers had only one hardwired floating point rounding mode, e.g. away from zero as in PDP-11 (page 154 of PDF).
Which historical architectures were the earliest ones to cater to the need for the ability to switch floating point rounding modes in software? Not necessarily at the same level of detail as IEEE 754, just two different modes switched by flipping a bit in a status register or using different opcodes would be enough.
A data point: M-20, designed in 1955-1958, had different arithmetic instructions for operations with or without normalization or rounding.