Even Vishnu has mantras like "OM LAKSHMI NARAYANA NAMAHA" but what is the famous mantra for the couple SHIVA/PARVATI?
I have not came across any specific mantra for the Shiva/Parvati. But I think this is you are looking for so far.
Karpur Gauram Karunavtaaram is an ancient Sanskrit Shloka related to Lord Shiva, and a popular aarti in Shaivism. शिवयजुर्मन्त्र
संसारसारं भुजगेन्द्रहारम् |
sansārsāram bhujagendrahāram |
सदा वसन्तं हृदयारविन्दे
भवं भवानीसहितं नमामि ||
bhavaṁ bhavānīsahitaṁ namāmi ||
karpūragauraṁ:- The one who is as pure as camphor.
karuṇāvatāraṁ:- The personification of compassion or the embodiment of compassion.
sansārsāram:- The one who is the essence of the world
bhujagendrahāram:- The one with the serpent king as his garland
sadāvasantaṁ hṛdayāravinde:- Always residing in the lotus-like heart (Explanation: Hridaya aravinde means 'in the heart that is (as pure as) lotus'. Lotus, though born in the muddy waters, is untouched by the mud around it. Similarly Lord Shiva always (Sada) resides (vasantham) in the hearts of beings which are not affected by worldly matters.)
bhavaṁ:- To the Lord
bhavānīsahitaṁ namāmi:- Accompanied by the Goddess Bhavani (form of Parvati, Shiva's consort), I bow
I assume that you are seeking Uma Maheswara Stotram written by Adi Shankra, check the portion below, click here for complete Stotram:
Nama Sivabhyam, Nava Youvanabhyam, Paraspara slishta Vapurtharabhyam, Nagendra Kanya vrusha Kethabhyam, Namo Nama Sankara Parvatheebhyam
Salutations to Lord Shiva and Goddess Shivaa, Who are always in fresh stage of youth, Who cling to each other in tight embrace, Of whom one is the daughter of the mountain, And the other is one whose symbol is a bull, Salutations and salutations to Lord Sankara And to that Goddess Parvathy.