By the way, as I said the integer spin functions are known. For example, (in terms of spherical harmonics) a SU(2) spin 2 function representation of a spin 2 object with a z component of spin 1 would be:
All I know about a spin 1/2 function representation of an object with a z component of spin +/- 1/2 is that it cannot be represented using the spherical harmonics. (Using two methods we can derive two different differential equations to obtain solutions which contradict each other.) Being that the integer spin representations and the spin 1/2 representations of SU(2) are irreducible, you might have expected that.