In the other thread Ravi Sri has given this valuable information.
"#20 - RaviSri
Re: Meeting of Trinities » 14 Jul 2012 19:12
Govindaswamy, Thyagaraja's grandson Thyagarajan and his wife Guruvammal did not have children. Thyagarajan (the grandson) died early, according to Subbarama Dikshitar, in his 35th year, which must probably be around 1865. After the death of Seethalakshmi, Thyagaraja's daughter, Gurvamma came to her ancestral house in Thanjavur in the year 1897, carrying the icon of Rama that Thyagaraja worshipped and a painting of Thyagaraja that a palace painter had painted. Both these are at Gurvammal's ancestral home on Varahappier lane in Thanajvur. The present caretaker of the icon is Sri.Thyagarajan who is a great grandson of Guruvammal's younger brother."
As per your clarification there is no direct descendent of tyAgarAja, alive.
If a portrait of the saint, painted by a court painter of tanjAvUr is available, this can be taken to be genuine. Can you make a copy of this original painting and post it in the forum. This painting should replace all other pictures of the saint, including the one painted by S.Rajam which is widely in use. The pictures in the number of books are as per the imagination of the artistes.
The statues at the saint’s samadi at tiruvaiyAru and tirupati are different. Any new statues, if made, should be based on this original portrait.