HTSeq package does that, it's based on python. It takes a gff3 as part of the input to define tags. Also, R package IRanges has a function called countOverlap, which also does the same thing, counting reads mapped to defined tags. Here, you may use a gff3 as input, convert it into a Granges object and count overlapped reads on top of that. I'd recommend the HTSeq solution if your bam/sam files are very large, as R tends to take the entire alignment at once. If you don't have a huge memory, you're out of luck.

Have you tried Cufflinks? It's pretty straightforward

http://cufflinks.cbcb.umd.edu/

You could also look up RUM (RNASeq Unified Mapper) as a complete mapping/counting solution for Illumina data.

coverageBed from bedtools can do it too.