Can we carbon-date the remains of homo floresiensis found in 2003?
ScienceMag says:


  Rather than damaging the fossils by dating them directly, the team looked to the sediments in which they were found. They discovered pieces of charcoal in sediments at similar depths, and considered those to be proxies for the ages of the fossils themselves. The charcoal bits were dated to around 19,000 and 13,000 to 11,000 years before present.
  But Liang Bau boasts a devilishly complicated geological history, as layers of silt and clay interleave with layers of weathered limestone, loose gravel, and volcanic ash. In many places, these layers have been scoured by erosion, altered by seeping water, and jumbled by tectonic activity.
  ...
  Dating on the gravelly sediment layer containing the fossils suggested it was deposited between 100,000 and 60,000 years ago; just above it is a layer of volcanic ash that was dated to about 60,000 years ago. This suggests that the fossils themselves couldn’t possibly be younger than 60,000 years old, the team reports online today in Nature.
  To cap it off, the team has now directly dated the fossils themselves. Originally, researchers shied away from that analysis for fear of damaging them, Tocheri says. But this time, they felt they needed to do it. “It wasn’t until [we] were reasonably convinced that [the fossils] were probably older than 50,000 years old that we decided we needed to date them directly to be absolutely certain,” he says.
  The team dated three arm bones found at different locations within the cave during previous excavations. Using uranium-thorium dating—which is based on the radioactive decay of uranium and thorium isotopes in a material—they found dates ranging from about 66,000 to 87,000 years old.


I could not find how the "charcoal bits" were dated, but it would be in the range for carbon dating.