Naval invasions aren't THAT hard 
Sweep first, send one or two ships head to make sure the path is clear. This is easy since embarked units are sloooow.
Keep a couple escorts near the convoy but not right on top of it, spread them out so you have more visible areas around them so you will spot hostile ships well before they are in range to sink your valuable units. Again, embarked units are very slow so your faster destroyers can easily reposition around them to respond to any hotile ships you find.
If you can't kill other ships... I don't know- are you using fresh, un-promoted zero xp units? My destoyers one-shot caravels with Targetting III, frigates might take two hits, sometimes not and other destroyers are done in 2-3 hits. If you plan ahead having a highly promoted navy is easy, caravels with targeting, sentry and mobility promotions upgrade to destroyers and frigates with bombard, sentry and range get upgraded to battleships. Only my subs and carriers start fresh.
For the invasion you have a lot of options to make it easier. You don't need a massive army first of all, even on huge maps. You also don't need them to all charge in at once unless you're invading a small continent or island. I like to send in a small force of highly promoted units with the objective of simple grabbing a piece of land and holding onto it. Once that beachead has been expanded I'll start ferrying over the rest of the army. The toughest part of the fight is going to be the target's initial response to your landing so pick somewhere easy to defend and outside of any city's bombard range.
Also, don't forget city states. If you can get a bonch of city states near the target to be your ally they make for a great distraction and may provide you with a good site the stage your invasion from. Worst case- they get conquered, but that's not so bad as then you can liberate them

Sweep first, send one or two ships head to make sure the path is clear. This is easy since embarked units are sloooow.
Keep a couple escorts near the convoy but not right on top of it, spread them out so you have more visible areas around them so you will spot hostile ships well before they are in range to sink your valuable units. Again, embarked units are very slow so your faster destroyers can easily reposition around them to respond to any hotile ships you find.
If you can't kill other ships... I don't know- are you using fresh, un-promoted zero xp units? My destoyers one-shot caravels with Targetting III, frigates might take two hits, sometimes not and other destroyers are done in 2-3 hits. If you plan ahead having a highly promoted navy is easy, caravels with targeting, sentry and mobility promotions upgrade to destroyers and frigates with bombard, sentry and range get upgraded to battleships. Only my subs and carriers start fresh.
For the invasion you have a lot of options to make it easier. You don't need a massive army first of all, even on huge maps. You also don't need them to all charge in at once unless you're invading a small continent or island. I like to send in a small force of highly promoted units with the objective of simple grabbing a piece of land and holding onto it. Once that beachead has been expanded I'll start ferrying over the rest of the army. The toughest part of the fight is going to be the target's initial response to your landing so pick somewhere easy to defend and outside of any city's bombard range.
Also, don't forget city states. If you can get a bonch of city states near the target to be your ally they make for a great distraction and may provide you with a good site the stage your invasion from. Worst case- they get conquered, but that's not so bad as then you can liberate them
