I do not have experience specifically with islets of Langerhans, but it is certainly possible to extract and purify DNA from FFPE tissue for specific cell groups. Here is a general protocol:
1. Select an appropriate FFPE tissue block by reviewing an H&E slide (make sure to match the slide to the block to get a general idea whether the slide is going to be representative).
2. Circle the tissue of interest on the slide (islets of Langerhans)
3. Identify the area of interest on the block
4. Punch out the area of interest on the block (example tool: Biopsy punch; Cardinal Part # AC3331AP25 (1.5MM punch))
5. Transfer tissue punch to tube and incubate/vortex in deparaffinization solution (example solution: Deparaffinization Solution (16 mL); Qiagen Part # 19093)
The rest of the protocol may include proteinase and RNase treatment, etc. before DNA extraction.
Note: Given that the tissue on the slide is only a "two dimensional" view of the tissue, your actual punch will likely include non-islet tissue deeper in the block. Laser capture microdissection from a slide will allow one to be pretty selective in the tissue obtained for DNA extraction, but obviously requires more specialized equipment.