1. With the child's complete DNA or key markers, I bet we'll eventually have algorithms for DNA -> adult phenotype
2. With only parental or relative DNA, if we are able to gather an enormous amount of extra information -- social group, gym use, hobbies, dating circles (mate selection probably yields a huge amount of info!), profession, fashion purchase activity, etc. -- then I bet we can get pretty reasonable confidence intervals on a lot of physical characteristics. Height, eye color, eye distance, face shape, lip thickness, etc. etc. Perhaps even elements such as voice timbre, etc.
If we had their familial phenotypes, photos and phenotypes of all a person's dating history, then I bet that lets us cut the search space down tremendously. If we add music listening habits and hobbies, I bet we'd also be able to cut it down.
I'm hypothesizing that physical appearance might correlate from behaviors, social graph information, and limited DNA information. I have nothing to show for that, however. (I would love to read literature on this topic.)
I'd imagine that constructing such a predictive model would require an enormous amount of data. Facebook + 23andme could probably pull it off.