use GOA to download all the RNA binding proteins (see this post: The Quickgo/Gannotation Api )

$  curl -s "http://www.ebi.ac.uk/QuickGO/GAnnotation?tax=4932&relType=IP=&goid=GO:0003723&format=proteinList"  

DB    ID    Symbol    Name    Synonym    Type    Taxon
UniProtKB    A6ZKQ9    MRPL16    Mitochondrial ribosomal large subunit component    A6ZKQ9_YEAS7|SCY_0179|MRPL16    protein    307796
UniProtKB    A6ZKR5    HEK2    Heterogeneous nuclear rnp K-like protein 2    HEK2_YEAS7|HEK2|KHD1|SCY_0185    protein    307796
UniProtKB    A6ZKS4    NCL1    M5C tRNA methyltransferase    A6ZKS4_YEAS7|NCL1|SCY_0194    protein    307796
UniProtKB    A6ZL23    RPG1    Translation initiation factor eIF3 subunit    A6ZL23_YEAS7|SCY_0293|RPG1    protein    307796
UniProtKB    A6ZL27    SCY_4021    Conserved protein    A6ZL27_YEAS7|SCY_4021|SCY_0297    protein    307796
UniProtKB    A6ZL63    TEF2    Elongation factor 1-alpha    A6ZL63_YEAS7|TEF2|SCY_0333|TEF1|SCY_5792    protein    307796
UniProtKB    A6ZL64    MUD1    U1 snRNP A protein    A6ZL64_YEAS7|MUD1|SCY_0334    protein    307796
UniProtKB    A6ZL74    SHE3    SWI5-dependent HO expression protein 3    SHE3_YEAS7|SHE3|SCY_0344    protein    307796
UniProtKB    A6ZL85    MAK5    ATP-dependent RNA helicase MAK5    MAK5_YEAS7|MAK5|SCY_0355    protein    307796

for DNA binding proteins: use GO:0003677 and remove transcription factors binding ( GO:0008134 )

Just came out: CISBP-RNA Database: Catalog of Inferred Sequence Binding Preferences of RNA binding proteins

And the paper in Nature: http://www.nature.com/nature/journal/v499/n7457/full/nature12311.html

There are some entries and motifs for S. cerevisiae in this database the RBPDB here is the link to the paper. Otherwise you may have to curate a list yourself from literature?

EuRBPDB (http://eurbpdb.syshospital.org/) may be the RNA-Binding protein database you needed, it provides the complete RBP catalogs of a large amount of eurkaryotes including human and yeast.