I'm finding the jump from Prince to Monarch pretty tough, it's about my 3rd or 4th game now and things are looking ok at the start of the Industrial era. In each of these games though, the Dutch have been there and also been the clear leaders; in my current game they are very close behind me in score and land/population, whilst being several techs ahead and having a far larger and more advanced military... scary stuff.
Aggressive tech-trading is a must (so try and get Alphabet quite quickly): you will almost never get a favourable deal, and prior to Currency do not be afraid to make unfavourable trades such as Writing for Priesthood. Once you get Currency you can make 'fairer' deals by getting either yourself or the AI to fill in the gaps in 'beakers' (they're flasks really but hey) using gold, but I believe that the AI will still demand some kind of favourable deal, such as you give them 5% more than they give you?
I agree with some of the posters here that I can start out reasonably strong, and maybe with the help of a tech lead expand peacefully/otherwise. I like expanding towards my rivals, and leaving myself space to 'back-fill' as soon as I can afford more cities - this allows me to develop a large, manageable empire whilst keeping my military on one front if possible. At around the Industrial times though, I start to seriously lag behind in tech and that smug little Willem is prancing around with tanks before I even get together any serious number of infantry! This time though I'm gearing myself a lot more towards espionage, and plan to keep tabs on Willem so things don't get that out of hand. Also, Diplomatic Victory is disabled, so I might actually get to use nukes for the first time!