(Like the Piano and junk)About an hour ago we received a call from the agent that the other bidder provided a counter offer and that we could also counter if we wished.

If after going thru the numbers with your seller, they still feel your initial offer is too lowball, I would look their motivation, perhaps come up with a counter offer that's a couple of grand higher and take a lower fee for the sake of closing the deal.

Hello BP,   I have just received a counter offer - which to my surprise, is from a Chapter 7 Trustee.   

Counteroffer from Seller = $187,600         Tri-Plex with a garage are currently renting for $2200 a month.Brief Description: Built in the 1900's.

There was but, in the counter offer, that was crossed out.

Somewhere in the 270-295k range in hopes of getting a good deal on it or at least a good counter offer.

And maybe thoughts on a highest acceptable counter-offer (assume my budget has enough room for $130k)?

Most likely that's what will make the seller happier about taking the offer, but I wasn't going to offer that right off the bat, though I'd make it part of the counter offer afterwards

The sellers have counter offered asking for an additional $50,000 earnest money deposit after the inspection period.

So you are less than a week away from closing and the buyer hasn’t responded to your “counter offer” (did it have an expiration date on it).