We consider Lord Mahavishnu as having ten avatars because they descend to this material plane (Earth).
Doesn't that apply to Lord Ayyappa who is the son of Lord Shiva & Vishnu? Shouldn't he be an avatar of Lord Vishnu?
Ayyappa isn't an Avatar of Vishnu, rather his son in union with Shiva.
Quoting the official website of Shabarimala
Lord Ayyappa  is known as hari-hara suthan, i.e. the son of Hari and Haran. Hari being Vishnu, and Haran being Shiva.
Vishnu took female avatar as Mohini  to kill a demon, Bhasmasura and also to acquire the amrit , or the elixir.
In this avatar, he mated with Shiva, and the child is Ayyappa. He was then adopted by a King.Since he is Vishnu's son, and not an incarnation of Vishnu himself, he is not regarded as an avatar
The difference between a descended avatāra and a foolish embodied being (dehī) is that avatāra does not forget his spiritual identity in the process and maintains a strong connection with the spiritual plane. E.g. in the Kurukšētra battle Krišna was hit by all kinds of divine weapons, including one that Arjuna could not possibly deflect, but Krišna did not suffer. He could just absorb the weapons, himself being unarmed. Likewise, any avatāra is expected to manifest at least some exceptional supernatural prowess.
In Chaitanya-Charitāmrita 2.20.365 Sanātana Goswāmī asks a tongue-in-cheek question "Who is the avatāra in Kali age?". The question is amusing, because he is asking it to that avatāra himself and they both know that. However, the Master answers:
To summarize his answer, an avatāra is recognized by the principal (mukhya) and superimposed (gauna) symptoms. In an avatāra, the manifestation of (divine) energy is direct (sākšāt-šaktye), if it is just a semblance (ābhāse), the person is called "vibhūti" instead. The symptoms to be looked for are described in the šāstras by muni Vjāsa (primary symptoms: name, skin color, dress, place of residence; divine energies: knowledge, love, the powers to create and maintain worlds and to protect and destroy villains; superimposed activities: killing of demons, creation, maintenance and destruction of the worlds and other). He also goes on to mention some avatāras and to describe the qualities and pastimes of Krišna in detail.
while we have not discovered a description in šāstras of Lord Ayyappa as an avatar of Lord Mahavishnu, we cannot accept him as such.