Actually, Jake King's answer is not quite correct.
Spoutcraft uses a copy and paste method to get minecraft.jar in its bin folder. It copies from wherever you have minecraft.jar on your PC, makes sure it's the same as the one on minecraft.net, and uses it like that. This allows it to check that a minecraft.jar is vanilla without breaking the ToS and distributing minecraft.jar. If you don't have a vanilla and up-to-date minecraft.jar, then the Spoutcraft client won't work.
What I think should happen is: delete everything that solar connects to Spoutcraft. Download it again, but make sure your computer doesn't enter sleep mode to ensure the download completes uninterrupted. Use two different port applications and port forward a modified Spoutcraft with your mod in it to yourself. (If you don't know how to do that look it up.)
Then, replace it in your applications folder or jar file. next go get you mod put in the addons folder in Spoutcraft and go to bin\minecraft.jar. Turn it into a folder with minecraft.jar as the folder name, then drag and drop to replace the mod into minecraft.jar folder and the mod should work properly.
To recap: what just happened is that since you port forwarded the same application, it automatically sets the default, making it seem like the it's the default app and "unmodified," giving permission to use it from Spoutcraft's code. Since the spoutcraft.jar file has the mod installed, making the reference look exactly like the minecraft.jar with the mod installed, it will pass the check and let you play. The only downside is that if you want another mod, you will have to do this all over again, but including the other mod this time.