Hey Anthony, welcome to the forum!
You didn't mention the PLC but if you just want to trigger a counter purely when a DINT changes value, do some thing like this:
If DINT <> TEMP Then Count
TEMP = DINT
So in the Logix platform (Compact/Control) you might have a NEQ OTE MOV on a rung all in series. NEQ will have DINT and TEMP, OTE will trigger your counter and the MOV will make DINT into TEMP. Basically your OTE will trigger for one scan, which you can trigger your counter with.
Or you could have NEQ ONS MOV with a similar setup descirbed above and use a XIC from the ONS to trigger your counter.
Or you could use a GSV to get the PLC time, which will store in a 7 DINT array, one element being the numerical value of the day of week. When the day is = the day you want, trigger your counter
If you happen to be using the Logix platform, try them all and see which one you like. I'm sure there are plenty of more ways to do it. If not the Logix platform, hopefully this will get you close
edit: Or I guess you wouldn't even have to use a ONS or OTE in my first two examples, you could just put the NEQ in front of your counter, then on the next rung, just make TEMP equal to DINT.
edit2: if none of that made any sense, let me know and I'll try to do better!