Sure. Usually, as you know, if you're buying directly from the owner, you have to pay all cash (or mostly in cash)--at least that's the way it is in most parts of the country. If you're buying new, then traditional financing (like a car loan) is used, and, yes, that could be a problem. But the price spread between a new mobile home and a used one is so great that most people buy used.
Now, if you don't have the cash, you'll have to find someone to finance it. It might be the current owner...or it might be an investor. There are a number of strategies that real estate investors use (even though a mobile home not permanently attached is personal property, not real property) to serve that market. Google "Lonnie Scruggs"--a big name in mobile home investing--for more information. But, basically, the investor buys the mobile home for cash at one price, then offers it on terms to the ultimate buyer. What most buyers are concerned about is finding a place to live that they can afford. They don't much care how the underlying financing is structured.
So, in a hypothetical deal, an investor buys a mobile home for $10,000 in cash. He then find a buyer with a few thousand dollars to put down--let's say $3,000. He sells it to a buyer for $3,000 down, $20,000 total at maybe 15% APR. Remember, the 15% APR is on the $17,000 owed by the buyer...even though the investor now only has $7,000 left invested ($10,000 minus the $3,000 down payment). The loan is structured for as long as it takes to keep the payments affordable--3 years, 4 years, etc. It's a good deal for the investor--some money up front and a very nice cash flow. But for you as the buyer, it's also a good deal. You get in for only a few thousand dollars and monthly payments that you can afford. And at the end of 3-5 years, you own the mobile home.
Yes, the investor will look at your credit, but the way the numbers work he won't be overly picky.