Are there any restrictions on trading stocks for others?

Generally speaking the type of service you describe falls under the titles of "broker dealer" and/or "financial advisor." Both of these titles are highly regulated at the state and SEC levels, with licensing and registration requirements. You may want to consult with an attorney as to whether your current "one-off" contract would fall into an exemption thereby sidestepping the above licensing/registraion requirements.

I hope that helps.

Disclaimer: This answer is for informational purposes only and does not constitute general or specific legal advice, nor create an attorney client relationship.