Do you always give in to your friends' requests?
If you don't you take a permanent diplo hit with pretty much everyone not just that civ. I'm careful about with whom I'll sign a DoF and tend to keep spare luxuries handy (since that's the first priority when they come begging). It annoys me that when the AI has a stronger empire than you they'll still say "things aren't going well over here, could you lend a hand"... when they've got more happiness, higher income and plenty of gold they still act like they need aid. And they need to remove that "I'll return the favor later" line since the AI never will give you handouts.
Back to warmonger penalties: In my current game, I encountered Japan, Morocco and Austria on my continent. Surprisingly, Japan was truly friendly (not just faking it like they normally do) and was the first to ask for a DoF. Since we were fairly close, I agreed. Later on Morocco approached for DoF. I was quite peaceful at the start (playing Mongols) since I needed to establish my infrastructure.
After a while both Morocco and Japan signed DoF. Austria was on the far eastern end of the continent and kept to herself. No wars happened for a while... then Morocco had the audacity to forward settle me (plopped a city right where I was going to put my fourth one between my capital and my second city - which I did put a bit away but I'd found the Fountain of Youth so I needed to settle near it). So I let the DoF expire then moved my units toward his city. Had the pop up about troops on the border so I selected Declare War. Using warriors, archers and a few chariot archers I managed to wipe out his forces and capture the city (Major penalty) then I accepted his peace request.
Austria and Morocco listed as having "early concerns". After a short while, Morocco's faded (they forgive modest warmongering while Austria hates warmongers). I decided I needed a 6th city, so I attacked Syndey (CS was pretty close to my second city at the Fountain of Yutes and they had access to Pearls). With my now experienced warriors, archers and chariot archers I made quick work of them since I got +30% bonus on top of my promos (and the Khan's medic ability combined with Faster Healing and March made my units almost unkillable). Syndey listed as Extreme warmonger penalty.
The next turn I was denounced by Austria (considered me a "global threat") while Morocco only listed as "seeing the potential threat of my warmongering". Japan kept renewing DoF.
A while later, Morocco dropped to "early concerns". Shortly after this decay, Japan asked me to join them in a war against Austria. I accepted and sent my scout division over there to farm some coin pillaging and maybe slaughtering a few wounded units (had full Honor). I actually found a level 1 city along the coast I was able to sack (Major penalty)... unfortunately, Japan negotiated peace the turn before I took the city, but I wasn't willing to relent until I sacked it (I'd made a few early misteps and was in bad economic shape... needed the coin from sacking the city since barbarian camps were getting scarce).
Morocco became guarded and listed me as "global threat". They didn't denounce me though. Japan let the DoF decay and after quite a while (was struggling into late Classical) Japan finally DoWed me... followed immediately by Morocco. Both listed as "seeing my potential threat" (yes, Morocco's penalty had decayed a bit by this time). Due to the terrain advantage (heavy jungle surrounding my starting location - great for defense but I was dead last in Literacy midway through Ancient) I was able to butcher large armies from both empires (and most of my units were obsolete because I was having funding issues and trying to get Markets up and running - that changed with the war since I started raking in the cash with each unit I slaughtered, my army is now the strongest on the continent and fully upgraded and I've just entered Medieval).
I have razed one Moroccan city (Minor penalty), captured one of Morocco's CS allies (Major penalty) and just took Marrakesh (Minor penalty)... neither Japan nor Morocco consider me a "global threat" yet (matter of fact, Japan now only has "early concerns" oddly enough). I'm running a slight economic deficit (-10 to -20 per turn) due to lack of external trade routes but I'm making plenty of money from pillaging, plunder and slaughtering units so I have no economic concerns right now. Plenty of happiness (Fountain helped greatly, but I now have a coliseum in all my cities) but I'm holding off on more captures until courthouses are built.
I have no intention of stopping this war until I own the continent (hopefully before explorers from the other continent arrive since all the unmet empires are 2-3 techs ahead of me as of last report and they all have 2-4 wonders each). After I finish with Morocco, I'm turning my full attention to Japan... then Austria... I'll probably sack a few more CS along the way. Now I'm not "steamrolling" them, it's slow, methodical advance. I spent quite a few turns whittling down Marrakesh with Chariot Archers while my melee units held a defensive line with archers behind to slaughter advancing units. By the time I had Marrakesh down to 1 hp, I'd slaughtered three waves of Moroccan defenders and just had a Horseman ride in and it had been so long since my last city capture that most of the warmonger hit had fully decayed from taking that CS.
Of course, I will pick up the pace in a bit. Either nearing Renaissance or simply getting Keshiks will put me in full battle frenzy until the continent is mine.