I would think of two approaches to detect and clone very rare noncoding RNAs (ncRNAs). The first approach involves the generation of a cDNA library. If you are interested in ncRNAs that bind to a specific RNA-binding protein, you can isolate this group of RNAs by immunoprecipitating the RNA-binding protein of interest. Alternatively, you can isolate RNAs that are <500 nt long (since many ncRNAs are much smaller than that) from the tissue of interest by denaturing PAGE. In both cases, the isolated RNAs would have to be reverse transcribed and a second strand synthesized to yield a cDNA library. Specific dsDNA linkers can be added after second strand synthesis so that the isolated  cDNAs can be directly cloned in standard vectors to create a library. The major caveat of this approach is that it might be inefficient or impossible to reverse transcribe your ncRNA of interest into cDNA if the ncRNA has a complex secondary structure, which would also result in the ncRNA being underepresented in the cDNA library compared to other easily transcribed ones. Finally, if your ncRNA of interest is not at all transcribed (at a specific developmental stage or under a specific experimental condition) then again you would not get it in the cDNA library. Such an approach is described and discussed more in detail in a very useful review on experimental strategies to detect/clone ncRNAs by Hüttenhofer and Vogel (Nucleic Acids Res. (2006) 34 (7), 635-646).
The second approach I would consider is a very sensitive antibody-based microarray assay for DNA/RNA detection as described and used by Hu et al (Nucleic Acids Res. (2006) 34 (2), e52). Typically, isolated RNA is either fluorescently-labeled or transcribed to cDNA which is then hybridized in DNA microarrays. Hu et al presented a method in which isolated RNA is directly hybridized to microarrays with no labelling or cDNA synthesis. They then use the S9.6 monoclonal antibody (Boguslawski et al. (1986) J. Immunol. Methods, 89, 123–130) from ATCC (http://www.lgcstandards-atcc.org/) which specifically recognizes DNA/RNA hybrids in a largely nucleotide sequence-independent manner and with high affinity and lacks reactivity to single or double-stranded DNA or to rRNA. Hu et al compare detection specificity and sensitivity to the cDNA approach for known ncRNAs and found out that the antibody approach was able to detect all of them whereas the cDNA method only 2/8. Signals above background were detected for less than a fmol of ncRNAs and sizes of down to 20 nt long. Altogether this antibody approach is very powerful for detecting small ncRNAs with potentially complex structures or modifications that are in low abundance. It is very important that the microarrays include the regions you are interested in (e.g., intergenic regions) or that you compare this type of analysis between microarrays under different conditions (developmental stages, different experimental conditions etc) so you can pinpoint ncRNAs that are upregulated and that would otherwise not be transcribed.