FS Marriott hotels tend to not have a lot of suite rooms. So given they aren't a stated part of the elite upgrade requirements and there usually aren't a lot of them, you just won't get them with regularity. Also, most "business" FS hotels in the US also tend to not have much difference in their rooms other than maybe an executive and/or a CL level. Given that, about the only upgrade they can really give you is a room on that executive or CL level or possibly a room on a higher floor. There just isn't much more to upgrade you to.

With that said, there are hotels (resorts, those with non-std designs, certain locations, etc) that may have rooms with better views, corner rooms with larger rooms, balcony rooms, specialty rooms, etc. At these hotels, there may be some decent upgrades to be had.

I mention all this first so we can set some expectations. With that, what can be done to help increase you upgrade chances (in those instances where there may really be something to upgrade you to)?

1. First, find out what types of hotel rooms a particular hotel has to offer. Decide what you would like to be upgraded to and specifically ask for that upgrade instead of asking for a generic "upgrade". The more specific I've been in the past, it just seems the more often I have been able to get what I wanted.
2. Find out the GM's email address and send an email asking about a possible upgrade. Let the GM know the reason you want the upgrade (i.e. honeymoon, anniversary, birthday, etc). The GM may send the request to one of their "reservation" managers, but it still tends to get more attention than otherwise because it was from the "GM". Also, this provides a chance at a pre-upgrade. Allowing you to know in advance what you are getting and not having to wait on check-in availability. Also, don't be too pushy in the email, let the GM know you realize that upgrades aren't guaranteed until check-in and that suite upgrades are a part of the normal elite benefits. But anything the GM can do to help out would be appreciated.
3. If you are traveling with your family, and you have younger children, bring them in with you to check-in. When my daughter was younger, I bet she got me a number of real upgrades just by waving and saying hi to the check-in person. I used to get all the "ooh, she's so cute, here let me see what I can do for you" line all the time.
4. When you are checking-in, be nice and actually try to talk a bit with the check-in agent. Ask them about what types of rooms they have at the hotel, maybe mention all the good things you have heard about the hotel and how you are looking forward to your stay. It just seems to me that the longer my conversations with the check-in agent were, the better my upgrade chances becomes. Maybe its because they get interested in the conversation and then become a little more friendly and then actually try to see what upgrades are possible.
5. I make all my RI reservations through the Plat line, not on line. I always ask the Plat agent to call the hotel and see if they can upgrade me to a 2 bedroom suite. (You can check online to see if the hotel has any 2 bedroom suites available before you call though.) I've had great success in not only getting a 2 bedroom suite upgrade, but they will quite often do the upgrade right then and there. ^
6. For CYs, just prior to check-in verify online that they have suite rooms still available. If so, at check-in ask about about a complementary upgrade to one of those suites. This year, I'm batting 100% on suite upgrades at CYs. I will admit that I don't remember ever being upgraded without asking though. So it is something you have to specifically ask about.
7. For other non-FS hotel chains, I would do something similar to my RI or CY upgrades.
8. Check-in times can also affect whether you might get a better upgrade or not. Some hotels may let you check-in early, but if you do that, even if the hotel is still selling upgraded rooms online, they may not have them cleaned and ready. You won't be able to get anything then.
9. One final thought. When you are getting ready to check-in, if it is a larger hotel with a couple of check-in agents, you might do a little "check-in agent profiling". I know profiling is an evil word and such. But if before you get into line to check-in, watch the check-in agents. You may notice one seems more cheerful and engaging versus another who is more "methodical" in checking people in.
10. OK, one more thought, if you will be returning to the same hotel often, spend time to get to know the employees there, especially the GM if you can. When I was doing a lot of international travels, I spent a lot of time at the Wuhan Ren and talked quite a bit with the GM there. It seems that he had been a GM at a few other Asia locations and knew the GMs at even more hotels. So I'd mention I would be visiting a particular hotel in Shanghai or Beijing, or Singapore, or where ever. He would mention he knew the GM there and would even call the hotel to get me some very nice upgrades, usually suite upgrades even. So networking can be a very good thing. ^

Good luck with you stays and potential upgrades.