Those plus your local state income tax withholding tables should be enough to get started on making something like this yourself.
The open tax solver linked looks good, but their payroll calculator assumes weekly pay which will get you in the ballpark but won't be accurate if you are paid less frequently (you can't even just double its numbers for biweekly pay, due presumably to rounding issues).
Py1040 looks ok as a start but will also only cover your end of year tax situation. It's also using hardcoded tax tables which is unfortunate since they seem to have been last changed in 2016 and so is wrong for 2018 and forward. Using external tables to drive it would make it much easier to update.
The IRS Withholding calculator will, of course, be very accurate but you can't really embed it into anything else. And if your tax situation is simpler you can elide a lot of details.