Is stationery countable or uncountable

It depends on how the Word paper is used. If you are referring to the type or class of substance that is paper, it is an uncountable noun. If you are referring some forms of paper, it is a countable noun. Examples:

Uncountable: Do you prefer paper or plastic. China is now the leading paper producing country. Use two pieces of paper to wrap each purchase.

Countable: These papers are published monthly. I had to submit two science papers this week.