Over the years I have had requests for a script like the Current Transits on the main page of the JyotishTools web site. Originally that script was written in PHP and maybe a little difficult for those requesting the script to implement. So recently I converted the script to JavaScript. It’s easy to implement and may be customized using CSS style attributes. It is available here with instructions for implementing.
The accuracy is about 1-2 minutes of arc and mainly varies on the Moon. To have the accuracy of a computer program would require a dedicated server and most do not have that kind of hosting. This script is run client side and just loads a small ephemeris for the month to calculate the transits for the current time.