Creating fillable minute field

Use the Number format and set the built-in Validation to only accept values between 0 and 59. Done.

And populating a drop-down is easy with a script, although I think it will be annoying for the user to have to select the exact time. You can do it in intervals of 5/10/15 minutes, instead.

This code will populate the drop-down will all the options, just change i++ in the for-loop to i+=10 to do it in 10 minute intervals, for example:

var items = [""];
for (var i=0; i<60; i++)
	items.push((i<10) ? "0"+i : i);
this.getField("Minutes").setItems(items);

1. Under 'Options' tab, select 'Limit of' and set to 2 characters.

2. Under 'Format' tab, select 'Custom' and as 'Custom keystroke script' use this:

    event.rc = /^\d*$/.test(event.change);

(this will allow only numbers to be entered into the field)

3. Under 'Validate' tab, use this script:

if (event.value !== "") {
var num = event.value;
if (num < 0 || num > 59) {
app.alert("Please enter a value between 0 and 59.");
event.rc = false;}
else
event.value = util.printf("%02d", num);}