What would be a fair estimate to have this 4 x 12 x 12 foot beam replaced under my 2nd story deck .It has wood rot?

that's going to be a toughie ... 4 x 12 x anything is custom milled lumber. May be better to replace with two or three 2 x 12 x 12 bolted together. Use pressure treated lumber. That's about $150 for the materials, including bolts, glue, and replacing the triangular braces.

Let the whole thing weather for a few months and then paint it next dry season.

The problem is going to be getting it into position without having the entire deck drop on your head. Calls for a number of jacks and a minimum two man crew. They're going to have to carefully jack up the entire structure in order to remove the damaged wood, then place the 2 x 12s, bolt and glue them together, then add the triangular braces, and then unjack the deck.

Sounds like a good four hours work to me, given the care required. Plus renting the capital goods [jacks and ladders], getting the lot there, cleaning up, etc. Throw in a risk factor [work on a ladder always costs more due to the risk of falling] -- maybe another ~$200 per worker.

so, call it $550 to $750 total.

Then you've got the issue of a contractor's license. You want a licensed contractor -- he has own insurance so an on the job injury isn't paid for by you. Look around for a local guy ... probably not a big outfit .. job's too small for them.

Maybe you could leave it in place and add another one bolted to it. Posts too.

Use bolts.

$40