Probably, if you exchange one co-op unit for another.
The question that would need to be researched is
can you exchange a co-op unit for another kind of
property, like a house, or a condo.
IRC Sec 1031 refers to exchanges of like-kind property.
I have seem some arguments about whether it will work
allowing you to exchange simply one kind of real estate
for another (i.e. land for land and a building).
The tax code - section 1031
The other part of that question is, when determining what
is like-kind property - is a co-op 'real estate'?
Or is it an interest in a partnership that owns a building?
If the title to co-op unit is as a partnership interest,
then, no, you cannot do a 1031 exchange.
Incidentally, why do you want to do the exchange?
If it was a personal residence, the first $250,000
($500,000 for married, joint, or two owners) of the
gain isn't taxable anyway. No need for the complications
or expense of a 1031 exchange.
If you need in depth research, please re-post your
question with the idea that it will take someone about
at least an hour to pull cases for you.
I hope this gives you a good starting point for your decision.