I am aware of Sri Yantra which is the yantra representation of Sri or Thirumagal, are there any other?
In my personal experience I have seen several types of yantras used by Sri Vaishnavas and in Pancharathra/Vaikhanasa temples. It would be a futile attempt to list them all for the reasons I will outline below.
A yantra is a physical manifestation of a mantra. The text of the mantra itself is etched onto a metal sheet (typically copper/silver/gold/panchaloha). The individual syllables of the mantra are positioned in certain patterns as described in Vedic/Agamic texts called Kalpas. Sometimes certain numbers are used. These are called "sankhya yantras". E.g. the Lakshmi Kubera Sankhya Yantram which consists of a 3x3 grid with all rows/columns/diagonals summing up to 72 like a Sudoku puzzle.
Asking for the number of yantras is similar to asking the number of mantras or the number of idol forms. Just like it is possible to have infinite unique forms of even one diety like Lakshmi Hayagriva, the number of mantras are infinite even for one diety like Lakshmi Narasimha.
For every mantra you know of, there is a corresponding yantra for sure. This is because in order to attain siddhi (mastery) over a mantra, one has to worship the deity using the method called purashcharya. This involves multiple acts such as (1) meditation/recitation (Japa) of the deity using the mantra several times, (2) performing homa with offerings with the mantra, performing kalasha japa (invoking the mantra deity into a vessel with water and performing japa), (3) performing thirumanjanam/abhishekam of the water on the idol of the deity, (4) worshipping the yantra associated with the mantra, etc.
The mantras commonly used by Sri Vaishnavas are :
- Nrisimha mantram (32 syllables)
- Nrisimha mantram (1 syllable)
- Sudarshana (6 syllables)
- Sudarshana (32 syllables)
- Garuda mantram
- many more Nrisimha and Sudarshana mantrams I have personally heard.
- Hayagriva mantram (1 syllable)
It is also common to see more than one mantra in a yantram. E.g. I have seen the Muralidhara yantram (referred to in the Gopala Vimsati) superimposed on the Sudarshana 6-syllabled yantram. Both share the common Pranava in the center while separate the actual mantra in different areas.
I have personally seen over a dozen different Nrisimha yantrams. The largest one I have seen was written on some kind of bio-paper with that was so fragile that the owner of the yantram did not even permit me to hold it in my hand. The yantram was about 3ft by 3ft square and written in Telugu script. The number of syllables written in it were easily over 1000. It was a Nrisimha Yantram and had several Nrisimha mantrams that I recognized. Much of the content appeared to be from the Nrisimha Tapaniya Upanishad.
Every ancient Srivaishnava temple you go to in South India is likely to have a few dozen yantrams and many of them are likely to be unique.
I have either heard all of this from my Acharya or am reporting my personal experience. I don't have a citable reference for any of this material