I'm not sure what you've tried to do before, but here's what I just did and had success:
1) Downloaded the Tomcat 5.5.27 Windows Service installer and installed it.
2) Dumped the TomCat5 service security descriptor using "sc sdshow tomcat5", which showed me:
This is a pretty common security descriptor for services. I've seen it verbatim on some Microsoft services. The SYSTEM and built-in Administrators have "full control", "Power Users" can stop, start, and pause the service, and "Authenticated Users" can query properties of the service (I'm glossing over a bit here).
3) I created a limited user called "bob" on my box, opened a "RUNAS" command-prompt as him, and got his SID from "WHOAMI /ALL" (a command that's on Windows Server 2003 but not on XP... don't know about Vista and Windows 7 off the top of my head). I verified that Bob could not stop / start the Tomcat service (using "NET STOP tomcat5"). I received the same error you report in your post.
4) From my regular administrator command-prompt, ran the following:
sc sdset tomcat5 D:(A;;CCLCSWRPWPDTLOCRRC;;;SY)(A;;CCDCLCSWRPWPDTLOCRSDRCWDWO;;;BA)(A;;CCLCSWLOCRRC;;;AU)(A;;CCLCSWRPWPDTLOCRRC;;;PU)(A;;RPWPDT;;;S-1-5-21-1409082233-484763869-854245398-1009)
This SDDL string gives Bob's SID (S-1-5-21-1409082233-484763869-854245398-1009) rights to stop, start, and pause the service (RP, WP, and DT, respectively).
5) I flipped back to my "Bob" command prompt and verified that I could now stop and start the service using NET STOP and NET START.
I'd recommend creating a group to delegte this right to, putting a user in that group, getting the group's SID (using WHOAMI or any other tool) and modifying the security descriptor this way.
I would think that using Group Policy to modify the security descriptor would work fine. I have seen cases where some services don't like the default permission that a group policy-based modification puts on a service (look at this posting about the Windows Search service if you want to see what I'm talking about: http://peeved.org/blog/2007/12/07), but that has been uncommon in my experience.
If you want more background on security descriptors for services, have a look at http://msmvps.com/blogs/alunj/archive/2006/02/13/83472.aspx and http://support.microsoft.com/kb/914392.