Carbon stars and DZ white dwarfs are two types of rare objects in the Galaxy. In this paper, we have applied the label propagation algorithm to search for these two types of stars from Data Release Eight (DR8) of the Sloan Digital Sky Survey (SDSS), which is verified to be efficient by calculating precision and recall. From nearly two million spectra including stars, galaxies and QSOs, we have found 260 new carbon stars in which 96 stars have been identified as dwarfs and 7 identified as giants, and 11 composition spectrum systems (each of them consists of a white dwarf and a carbon star). Similarly, using the label propagation method, we have obtained 29 new DZ white dwarfs from SDSS DR8. Compared with PCA reconstructed spectra, the 29 findings are typical DZ white dwarfs. We have also investigated their proper motions by comparing them with proper motion distribution of 9374 white dwarfs, and found that they satisfy the current observed white dwarfs by SDSS generally have large proper motions. In addition, we have estimated their effective temperatures by fitting the polynomial relationship between effective temperature and g-r color of known DZ white dwarfs, and found 12 of the 29 new DZ white dwarfs are cool, in which nine are between 6000K and 6600K, and three are below 6000K.