A small change in your terminology may help. When talking about relays and someone says they want a relay that can handle XX, most people will think about the rating of the switched contact not the control signal.
It may be more clear to say that you need a relay that will
operate from XX volts and
switch XX volts and current.
As you may know not all solid state relays will switch DC. A lot of solid state relays use thyristors and they will not switch DC. There are solid state relays that use power mosfets for switching and they will switch DC and the manufacturers will specify that they will switch DC.
"The input amperage is very minimal."
The input current (the current used to control the relay (solid state or mechanical) will be determined by the device used. It can vary.
A quick look at some of the solid state relays showed a range of just a few milliamps to as much as 25 milliamps. The control voltage tends to vary with the control voltage, the higher the control voltage the higher the control current. This is the amount of current needed to control (switch on) the solid state relay. Just something to keep in mind.
Since you mentioned solid state relays, I found this solid state DC switching relay at
Jameco. Its control voltage is DC not AC, but it will switch DC. If you rectify your AC control voltage, it looks like this device will need around 20 milliamps of control current to turn it on.
I took a quick look at some of the larger parts houses such as Allied Electronics and found similar things to the Jameco part. I just took a very quick look, some of the larger parts houses may have solid state relays that can be controlled with and AC voltage and switch a DC voltage. It may be worth a look or maybe someone here knows of a specific part. It has been awhile since I have had to do any specing of parts.
I took a quick look at AC coil mechanical relays and there are a lot of 24 volt AC coil relays and they are small enough to meet your requirements but they need north of 35 milliamps to operate. I know there are some sensitive AC coil relays out there, I just did not stumble across any.
I do not know if needing 15 to 30 milliamps or more to operated the relay (solid state or mechanical) will be an issue for you.
Again, and I may have missed something, but I seem to be the only one that has mentioned that not all solid state relays will switch DC.