The carnatic raga Yaman Kalyani is a very close variant of Kalyani. That is, Yaman Kalyani is a janya raga (derived raga) of the melakarta raga Mechakalyani. The derivation is a result of addition/deletion of swaras (notes --sa, ri, ga, ma, pa, da, ni) to the characteristic pattern (Arahonam/Avarohanam) of the Melakarta raga. Other interesting janya ragams of Kalyani include the beautiful Hamir Kalyani (or Amir Kalyani), Saranga, Mand (or Maand), Behag (or Bihag), Mohanam (the latter ragas could have alternatively been derived from another hugely important raga Shankarabharanam).
The poetic liberties taken by the modern music directors often make it difficult to discriminate the raga for film songs and this is particularly true for close ragams like Kalyani, Yaman Kalyani (or Hamir Kalyani and Saranga, Madhuvanti and Dharmavathi -- which will be the subject of a later post).
One very popular Kannada kriti "Krishna Nee Begane Baro" set in Raga Yaman Kalyani is frequently sung in carnatic music concerts as "Thukkada" (a tiny piece). This one is sung by maestro Maharajapuram Santhanam.
Here is a fusion music piece of the same kriti "Krishna Nee Begane Baro" in Yaman Kalyani sung by Hariharan in a Live Concert.
The song "Thamizha Thamizha" from the movie Roja sung by Hariharan is one of those songs where shades of Kalyani and Yaman Kalyani make it hard to discriminate:
The song "Varaaga Nadhi" from the movie Sangamam sung by Shankar Mahadevan is set to Yaman Kalyani.
Here is a nice elucidation of Raga Yaman (the hindustani equivalent of Kalyani and indubitably the rationale for the existence of the carnatic Yaman Kalyani) by the Sarod Virtuouso Ustad Amjad Ali Khan. In this clip, Ustad Amjad Ali Khan illustrates his vocal talents too: