It is true that Lion and Tiger are associated the most with Maa Parvati. She is Simhavahini and Vyagra vahini. Primarily, lion is the vahana of Goddess Durga, but tiger is also associated with her in some of the forms.
Now let's see the other vehicles of Maa Bhavani, apart from lion and tiger.
- Nandi 🐂
Nandi is the vahana and the great devotee of Bhagwan Shiva. Being the wife of Shiva, Maa Gauri also has Nandi Deva her vahana.
2. Donkey 🫏
In her one of the most calm and gentle forms Sheetala, Goddess Parvati has donkey as her vahana. Also, in one of her fiercest form Kalaratri, she has donkey as her vahana.
3. Goat 🐐
Parvati as Maa Meldi has a goat as her vahana. This form of Mahadevi is mostly worshipped in Gujarati tradition.
4. Chicken 🐔
In her Bahuchara Mata swaroop, Goddess Parvati has a chicken as her vahana. She is mostly worshipped in Rajasthan.
5. Elephant
Although elephant is associated with Goddess Lakshmi and Lord Indra, during last year's Navratri, elephant was called the mount of Goddess Durga, but it's rare.
6. Wolf
In her one of the most terrifying forms Chamunda, Devi has got wolf as her companion.
7. Buffalo
Sometimes buffalo is also associated with her, though she slayed a buffalo demon Mahishasur.
8. Corpse
In her scariest version, Maa Chamunda has a corpse or a preta or a ghost as her vahana. Even in her Baglamukhi form, she slays an Asura and sits on it, that asura as a corpse serves as the vahana.
9. Betala
Maa Bhadrakali, another fierce form of the Great Goddess, she has betala has her vahana.
10. Crane
Sometimes, crane is also associated with Goddess Baglamukhi.
11. Mahadeva (not as some subordinate, but as the base for the divine energy).
Shankar Bhagwan is not actually vahana, despite being her Swami, he also serves her in multiple forms by acting as the base (aadhar) upon which Shakti functions, multiple forms of Goddess Parvati like Maa Kali, Tara, Kamakhya, Tripurasundari etc. are depicted in a way that she is seated on Shiva himself. Out of love for his Shakti, Shiva serves as the base and vahana or asana to be precise in that way.
There must be many more vahanas, but I remember these as of now. Bhagwan Shiva is Pashupatinath, being his consort, Maa Parvati also is associated with multiple animals who serve her as vahana.
Jai Bhavani 🙏 Har Har Mahadev 🙏