Using buttons to fill text field Acrobat DC

On a 'heads' button as 'Mouse UP' you can use:

this.getField("toss1").value = 1;

Change 1 to 0 for tails button.

What would be the point of autotab in situation with two buttons?

Here is a suggestion, you can make 1 button with custom script that will simulate toin coss and write appropriate word (Heads/Tails or 1/0) in toss fields every time it's clicked it will move to next field and reset fields once all fields are filled.

You should use buttons for this, yes. And setting the focus to the next field is not needed. What you need to do is scan the text fields (let's say they are named "toss1", "toss2", etc.), and fill the last one which is blank.

You can do it using this code as the Mouse Up event of the "heads" button:

for (var i=1; i<=5; i++) {
	if (this.getField("toss"+i).valueAsString=="") {
		this.getField("toss"+i).value = "1";
		break;
	}
}
if (i>5) app.alert("You can not do another toss.",1);

Simply adjust "1" in line #3 to "0" for the "tails" button, or to something else (not a blank value, though!) for the "other" button. For example, you can use "-".