I cant speak on a national level but in Texas inventory is low and competition is tough.

So I had to pay for another appraisal (that came back right in my range).Bottom line is that there has to be a better way to enforce some of the appraisal rules.

We're looking at buying a few apartment units or small SFH that are in the 50-75K range (ready to rent with minimal work) and are finding that most conventional lenders don't have interest in loans that small.

Do you have anything in your inventory that matches this description?  

It's a range using only a few factors.

I usually stick to SFR's but now with the thinning inventory, I started getting into some condos.

Where FHA deals can be more difficult, I am having trouble understanding how that alone is preventing your offers from being accepted and, where inventory is very low right now, suspect the $100k approval is what is limiting your choices most of all. 

There is a shortage for homes in the 100-200 range.

No inventory available.

Hard money/ private money would have relatively short period to provide loan in the 1-3 week range.