I own a 2 person LLC but my partner's shares were bought out by a new member about halfway through the fiscal year. What is the correct way to file the K-1s?

You need to go into the partner information section and  update the ownership.  By entering this along with the date it occurred, TT will perform the correct computation.

Make sure the former partner's K-1 is marked as final.

There are a number of issues that need to be addressed, so depending on the $$ involved you may want to consult with a tax professional:

• Are there any "hot assets" that need to be considered and that information provided to the former partner
• Did the new partner pay an amount in excess of book value in which case will the LLC make a Section 754 election to step up the basis of the assets
• If there is a step up election made, then you will need to make special allocations going forward

RE: Hot assets
I'm not sure I would classify anything as a "hot asset". There was a good amount of inventory and raw material at the time of the buyout, but the old partner received a large amount of the stock in addition to the monetary buyout. There were also accounts receivable, but the old partner had moved to another state and was incapable of assisting with ongoing/incoming projects. So, he conceded any claim to profits from any projects in which he wasn't directly involved.

RE: Book Value,  Basis
This is a very small side/start-up business---The new partner was basically an angel investor because the old partner had pretty much become dead weight. The valuation at the time was around $15K. The new partner bought the old partners shares (valued at about $7500) for $3500. The former partner never made any capital contributions but I contributed approximately $4000 out of pocket. I wasn't really considering changing the basis because the valuation is so low right now.

I do have a couple of other questions if you could assist further:

When adding the new partner TT asks for:
1) Last Years ending capital balance -- should that be the actual capital balance from the previous year or the balance at the time of the buyout?
2) Cash member contributed to the LLC -- I assume this means specifically contributions made after the buyout, correct?
3) Where exactly does the TT account for the actual buyout amount?

Additional comments:
1) Your definition of hot assets is most likely not the same as the IRS definition.
If you were using the cash method of accounting, then you have hot assets (accounts receivable).  Your inventory is possibly a hot asset.  Depreciation recapture is also a hot asset. This comes into play for the seller as this individual may need to reflect ordinary income for their portion of these items.
2) The facts are not clear as to whether or not the new investor paid the  old partner or infused the $$ into the company and you used those funds to redeem the old partner.  If the former, then the new partner just steps into the shoes of the old partner for book purposes.  Keep in mind this is not the same as tax.  This individual will need to maintain their own tax basis in this investment.
3) Not sure your questions 2 or 3 come into play, but as noted above, not sure how the buy out came about.

As you can see, this is complicated regardless of the value of the business.