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The Fossil Maniac's house near Fallarbor Town. His brother has the TM Dig.
Diglett is the only one that I think can learn Dig normally... but he is not in Emerald :/.
If you can't get the TM, your options are trading from FR/LG or catching a Trapinch. Trapinches are a pain, though, because they learn Dig at an ungodly high level, and you can't evolve them to do it.