I have been able to find AY (Finnair) and IB (Iberia) business awards online in the past, but they can be very hard to find.
BA awards are a lot easier to find because they have a lot of flights to the US and people try to avoid using them if possible because of the high fees.
I believe awards for some partner airlines aren't available online and will require you to use EF to check availability and then call AA to book, but I'll let the more knowledgable FT members chime in on that.