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.

Well this one is an extremely difficult task... Let me think if I can figure out any solutions...

a few of the larger registrars will offer suggestions on their order page, if the name you are trying to purchase is not available.

As far as the online software you tried not allowing you to save the results, you could save a screen capture instead and then transpose the info later.

you can save them in time when you get the domain result.

yahoo small business maybe help you, but it's has no software/tools with them.

Why you need software if you have your head? I usually use my primary keywords with Addons - some other words.

Are you talking about domain name generators? If Yes I would not recommend you using them. Use them to get some suggestion. The domain names it will generate for you are not really good to be used. Really.

I suppose such tool simple do not exist. If that had existed all good domain name s for all niches would have taken. That's it