As promised, here are some stardate apps and widgets.
V1.2 Nov 19, 2013 (56615)
This is an extension to DashClock Widget. It can display one of five types, with examples:
The Original Series: 1163.28 (1yy+month.day)
The Next Generation: -277553.08 (subtract about 915 per year from 2364)
Contemporary TNG: 69704.4 (add about 1000.0 per year to 1947 July 15)
Modified TNG: [-27] 3790 (see Andrew Main)
Star Trek (2009): 2016.88 (year.day)
V1.0 Jan 6, 2016 (57393)
This Italian app should show negative TNG stardates, but doesn't work.
V1.5 Feb 1, 2012 (55958)
It's supposed to have a calculator, but it crashes. However, the widget works. It displays Andrew Main's stardates, square brackets, negative numbers and all. There is an iPhone version.
V1.2.2 Oct 9, 2015 (57304)
This "stardate" calculator shows years with decimal fractions, with either 3, 6, or 15 decimal places.
V1.1.2 Jan 10, 2014 (56667)
The app has a nice icon and LCARS calculator, with an LCARS widget. Stardates can be either "24th century", which is a large negative number like -307236.7, or "unmodified", like [-4] 93236.7. The latter apparently increments 1000 per year from 1923, with the number in brackets the centuries before TNG.
Stardate calculator by NemoPeti
Dec 19, 2012 (56280)
This widget also shows negative TNG stardates with 11 decimal places. It has three buttons for refresh, copy and info (in Hungarian).
Sander van Kastreel
V1.0 Jan 9, 2013 (56301)
This LCARS calculator app increments 1000 per year from the beginning of 1955...except for the past few years it seems stuck between 58000 and 58999, when it should be 61xxx. It should go to 62000 next year, though.
StarDate for AlarmPad
V1.0 Jun 12, 2015 (57185)
An AlarmPad extension, which does not work for me.
V1.2.0.b1 Nov 7, 2014 (56968)
This is the best one I've seen. It has a beautiful LCARS app and 1 widgets, all of which display 5 different formats simultaneously:
TOS [-27] 3790.1028
There is also an info button that explains each one, and a help button that explains how to turn them on or off in the widget. The pro version also has buttons for calculating to-from stardates and calendar dates, and costs $1.96.
V2.0 Jun 6, 2014 (56814)
This app is actually a voice recorder, which displays the current stardate while recording so that you can speak it into you "captain's log". Stardates increment 1000 per year from the beginning of 1923.
Negative TNG: -306748.3
Star Trek Online: 93846.33