Carch is used for fang. Nen is used for water. -Nil or -Dil is used for friend/lover
In Quenya, the word Nendil (literally water-lover) means any water-animal.
I'm thinking Carchnendil, fanged water-lover.
Thoughts?
Let's look at the etymology of "crocodile." It comes from the Greek word krokodilos, meaning 'worm of the stones,' from krokē 'pebble' + drilos 'worm.' Using this, we can construct sarn, meaning "(small) stone, pebble; stony (place)," + leweg, meaning "worm," to give us Sarleweg. Alternatively, using the Neo-Sindarin gwem, we get Sarwem.
"Alligator" comes from the Spanish el lagarto, meaning 'the lizard.' For "alligator," perhaps using the idea of nen + lizard would give us Lhugnen. The reverse construction doesn't work.
Regarding Carchnendil, the sequence -chn- does not exist in Sindarin. I believe it would yield carnendil.