It sounds like you need a PLC rather than a motion card, unless a servo is involved.
There are also PLC type very small units called programmable relays that require no software or programmer, the same units are marketed under several labels.
Siemens, Idec, Omron etc.
They have limited I/O and timers latches etc and small instruction set.
BTW there is a very cheap way to implement simple machine control using some legacy Galil boards that are cheap in ebay.
It is not quite as fancy as some of the G code commercial systems for these boards, but very adequate in a lot of cases.
If you need more info. PM me.
Also with this project, do you need operator interface?
With a PLC, I use Maple Systems keypad/2 line display units, they will interface to most PLC and Galil cards.