I enjoy playing Denmark right now.... especially since I love being harsh and cruel to those Swedish peasant people
In the early stages of the game, Denmark should not fight Sweden directly.
You always have to be looking for opportunities.
A perfect "opportunity" is like when Russia savagely attacks Sweden because Russia wants to take Ingermanland. That means Sweden is distracted and all her good armies are fighting along the Russ border.
In the meantime, I built up Denmark's economic power by:
1) vassals vassals vassals!
Vassalize Saxony. They are very friendly to Denmark, very easy for Denmark to vassalize. Saxony are excellent vassals, since they are loyal and they have capable armies that fight well.
Vassalize at least one more country, preferably a country that is a neighbor of Denmark, e.g. Pommerania or Hanseatic League
2) Diplo-annex Holstein quickly! It's a rich province, plus it's nice when you inherit their army and fleet.
3) Create your own large alliance with local powers like Holstein, Pommerania, Prussia, Saxony, Hannover, Hessen and even Netherlands. Make sure that some of these allies are naval powers. That is important because most of the wars that Denmark will fight will require naval invasions!!
And then as soon as you see one of your "prey" become non-allied (i.e. they currently have zero allies)... have your entire Grand Alliance gang up on that nation. For example, you just saw that Teutonic Order's alliance with Sweden has expired. This now means that TO has zero allies, and it's even better that you have a CB against them. This is a perfect opportunity to declare war on them and call your 4 or 5 allies to help crush them. Don't go to war unless you are sure you can invade and successfuly take at least one or two good provinces. Take only rich provinces like Kurland (CoT). Taking poor provinces will not help the Danish economy.
4) Eventually you and Sweden will go to war. Sweden simply hates you, especially since Sweden has a free CB on Denmark, since Denmark occupies several Swedish CB shield provinces. Thus, Sweden will always view Denmark as an invader.
This means that even if you give Sweden money to be friendly, that friendship will NEVER last very long. The fact that you own several Swedish CB provinces means that relations will always deteriorate very quickly.
If however you are not yet ready to fight Sweden, simply do a royal marriage with them! Even when Sweden hates me and they have a large army on my border, Sweden never attacks when they have a royal marriage to Denmark.
Use the royal marriage as a delaying tactic, as a tactic to "keep them off your back".
You can royal marriage anyone if your relations are between -150 and -6 This is a glitch in the game, I think?
In the end, Denmark player must do something to weaken and partly cripple Sweden. You must look for opportunities, for example when Sweden is badly losing a war to Russia.... that's a good time to mass your Danish armies in Skane and make a blitzkrieg attack on Smalland and Stockholm.
Remember that whenever Russia fights Sweden, the Swedes will always leave Stockholm and their western provinces undefended! This is a perfect opportunity for Denmark.