I’m looking for a software program or a online site that finds
domain names for vary competitive niches.
I’m building a blogger blog in one of the most competitive
niches there is games.
I tried some of the domain search software programs but
a lot of them would not let me save the domain list.
I personally really like a site called bustaname that looks at combinations of words you specify. It does allow you to save your lists.
I love this website: http://domai.nr/
It looks for domain hacks (a great way to get quirky domains) 
Also you can try godaddy…it is quite good site for searching a domain names…