Since $(1+i)z=2i$,

We have $z= \frac {2i}{1+i} = \frac {2i(1-i)}{(1+i)(1-i)} = \frac {2+2i}{2} = 1+i$,

Hence, the conjugate of $z$ is $\bar{z} = 1-i$.

So the answer is: $\boxed{\bar{z} = 1-i}$.

This is obtained by manipulating the original equation and using the algebraic form of complex numbers to simplify the value. This question tests the understanding of multiplication and division operations with complex numbers in algebraic form, which is a basic concept.