It is possible to make a buffer that functions well near ph 7 using citric acid, which contains only carboxylate groups.

Yes, it is.

Explanation:

A buffer is a solution in which a weak acid is in equilibrium with its conjugate base, or a weak base is in equilibrium with its conjugate acid. Because of the equilibrium, when an acid or a base is added to it, the pH remains almost unaltered.

But the buffer has a limit, generally, it works well in the range of pKa - 1 to pKa +1. The pKa value indicates the force of the acid, and it's calculated by -logKa, where Ka is the equilibrium constant of the acid. The pKa value of citric acid is 6.86, does a buffer of it can function well at pH 7.

The successive deprotonations of the acid increase the "-" charge density on the resulting anion, in this case, the carboxylate groups. This is unfavorable electrostatic repulsions between the anions which reduces the likelihood that a proton would dissociate. So, it's more favorable for the proton to remain bound to reduce unfavorable charge repulsion. Because of that, the equilibrium can be achieved.