Create SPDT relay from two SPST solid state relays
Figure 1. The datasheetless SSR.

You haven't posted a link to the SSR datasheet. I found the image shown in Figure 1 so we know it will work with 3 V DC but don't know what current it will draw. You need to hook one up to a 5 V supply and measure the current in on pin 3. Then compare that with your micro's output specification. Typically 10 to 20 mA should be OK. Be careful to check what the output voltage will be at that current - the higher the current the more the output voltage gets pulled away from the supply rail.

SPDT SSR







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 2. A design worth trying.

How it works:


When GPout is low D1 is turned on and SSR1 will conduct. LAMP1 will turn on.
When GPout is high D1 will turn off, etc., D2 will turn on and SSR2 will conduct. LAMP1 will turn off and LAMP2 will turn on.


There is an interesting third state. 


If GPout is disabled (tri-stated or floating) both D1 and D2 will pass some current. According to the datasheet printed on the face of the device (it's all we've got) both SSR1 and SSR2 will fail to turn on and LAMP1 and 2 will turn off. At 3.3 V this should be quite reliable. At 5 V you might find that one or both stay on as there would be about 2.5 V across each one and 3 V DC would be a maximum for the minimum turn-on voltage (if you can follow that). 



  I'm trying to use two solid state SPST relays (P/N SAI4003D) to act like an SPDT relay. 


Requirement met.


  Ideally both will be controlled by the same signal wire. 


Requirement met.


  The relays state that they are "on" at 0 volts, 


I didn't find that information and don't know what it means.



Looking back on your question I think this was what you were trying to draw in your schematic. I couldn't make sense of it when I first read it. I think you were on the right track - although a little lacking in elegance? ;^)