Question

What ending should this word have? avail-

Answer 1

That depends. It could be:

available
availability
availably
availableness

I assume you were just going for -able versus -ible, in which case it is the first spelling. 

Answer 2

Answer:

The correct ending is able = available,

Explanation:

Between the options of possible endings "ible and able" we can say that the -ible ending is for words of Latin origin, meanwhile The -able ending is for some Latin words, non-Latin words, for example, and new (modern) words, then the word avail being an Anglo-French compound of Old French uses the ending able.