I wrote up a couple tools to generate random posets to use as examples. The below were made with 2 small perl scripts and the dot tool from graphviz (along with the tred tool to get the transitive reduction, also from graphviz).
Both of the below tools can generate a singleton poset:
SP.pl | tred | dot -Tsvg
Generates SP, or Series-Parallel posets, up to a maximum depth.
compose.pl | tred | dot -Tsvg
Generates posets by recursively composing in series, parallel, or through the 
poset. As N is the quintessential non-SP poset, in a certain well-defined sense, this gives a diverse selection of posets, if not all. 
