Tammy, short answer is often yes, but it really comes down to the lender's guidelines, so it's worth asking about it specifically up front.
A 681 is within most DSCR programs' minimum score ranges, though it will affect pricing and max LTV. On most non-QM DSCR programs a charge-off isn't treated like a foreclosure or bankruptcy with a long waiting period, but lenders differ on whether open charge-offs and collections have to be paid off before or at closing, especially above a certain balance.
The EIDL is the part I'd flag early since it's federal debt. Some lenders look harder at delinquent government debt, and if there's a judgment or lien that shows up on title, that has to be cleared before closing.
Things that can help: getting the EIDL resolved or onto a documented repayment arrangement before applying, paying revolving card balances well down before the statement dates (lower utilization usually helps the score), disputing anything on his reports that's actually wrong, and then having the lender run a rapid rescore once that's done. Adding a co-borrower with stronger credit is another route on some programs.
I'd have him pull his full credit report and confirm exactly how the EIDL is reporting (charge-off, collection, or referred to Treasury) before shopping lenders, since that drives the answer more than the score does.
You will need to provide a letter of explanation to the lender. Some of them will be fine with it. Others might be more hesitant and will scrutinize the deal further, so they may not give you as much leverage as you were anticipating or might structure the deal to be a little bit more conservative.
Yes you should be able to obtain DSCR financing as long as you are current on your client is current on their other loans and can provide a LOX. The key is presenting the file's strength and weaknesses entirely and working with a lender that can get past the file's weak points. Working with a broker helps tremendously, instead of exhausting time and money spent on appraisals working with lenders that are 50/50 about the deal..
Tammy, good question to ask on your investor's behalf — and the short version from what lenders here have shared is that a charge-off doesn't automatically rule out a DSCR loan, but the EIDL piece is the part to sort out first. A 681 credit score is generally in range for many DSCR programs, though it will affect pricing and terms, and every lender's guidelines are a little different, so it's worth talking to two or three investor-friendly lenders rather than taking one answer as final. Practically, I'd have your investor pull his full credit report, confirm exactly how the EIDL is reporting, and be ready with a clear letter of explanation and documentation on his other loans being current. Getting that file clean before applying saves a lot of back-and-forth — and underwrite the property conservatively either way, so the deal works even if the rate comes in higher than hoped.