As a general rule, if the stress points are not too stressed, you can use something like Weldbond wood glue. There is another substance called gorilla glue, which is a very strong all purpose glue, but expensive and difficult to clean up. So, the answer depends on who is using the glue and what they are making. I am not sure if there is a liquid nails appropriate for the application you are talking about. Weldbond is pretty strong, and cleans up well.
Liquid nails tends to be harder to clean up.
Dear Dr. Beast, There are large black bugs crawling out of the urinals at work. While this was sort of amusing in the beginning, it's become a nuisance of late. Soap poured down the drain does wonders if they're roaches. Beyond that, you could contact Tom Ray, who used to be big in bathrooms. While US Standards indicate that few, if any of us, are in danger, Soviet standards are considerably more stringent.