You have banks ( local,regional,national), credit unions, life insurance companies, & CMBS lenders.Who does what loan depends on location, asset type, and size of the loan.

I assume  you want  to improve (rehab) it to a B property. 

b) Buy/rehab the property5 - After the "seasoning period" required by your lender, get the property refinanced.6 - Take the cash from the refinance (this is why you use cash to start with...and not a loan) and repeat Steps #4 - 6...as many times as you want/can.Note: After a certain point, or even in the beginning, you may need to involve cash partners to get the needed cash together, or a credit partner if you can't get approval for the refi's.For me I didn't have the cash to put down, so I used a hard money lender.

-What's a reasonable credit requirement for this [lower income side] area?

I've heard that First Citizens has good products, as well as SC Federal Credit Union.

I'm currently stuck and do not have any way for traditional funding and my credit is to low for other methods.

I'm newish to Houston and looking to shift my investments from appreciation plays (4 or less units) to Mom and Pop Multi-Units that could use improvement.   

I'm currently stuck and do not have any way for traditional funding and my credit is to low for other methods

Rental Agreement + Option to Purchase AgreementRental Agreement: a typical lease agreement with the total amount of rentOption to Purchase Agreement: this includes all the terms of the Lease Option such as Final Purchase Price, NROC (see below for more details), and how much of the rent will be credited back as rent credits (I typically charge above market rents and use that extra amount as rent credits).I have the Tenant-Buyer sign both of these docs and pay me the Non-Refundable Option Consideration (NROC).

A bit risky, but it worked.Having said all the above, I did not have the complication of a mortgage on these properties because I used line of credit funding on my principle residence.