Immigration Magnet Strategy
With any immigration-magnet country, your strategy should be broken down into 3 phases: Pre-Immigration, Immigration, Rule The World.
Pre-Immigration, you should be focused on increasing your RGO output and keeping a balanced budget as well as saving up money for the second phase. You should stay with a monarchy or a presidential dictatorship if you start in one. Either way, you should work to keep a conservative party in power (not hard since most of your people will be farmers and laborers). This is to keep militancy down, since democratizing will upset a large number of your (largely conservative) POPs. Focus your research on commerce and some industry techs. The big ones you really want is "Freedom of Trade" if you start without it and "Mechanical Production". Both raise your output for most RGOs by several hundred percent. If you have any iron or coal provinces, Clean Coal is also a must, raising coal and iron production significantly. However, as soon as it is available, research "Ideological Thought". This is so that the -25 plurality from the 5 conservative "Ideological Thought" inventions has the least impact on your plurality, which needs to be high to get large amounts of immigrants. This phase is over once you have a nice export income and a budget surplus, as well as a nice slush fund ready (around 50-100k is nice depending on how fast you want to implement phase 2 and your starting population.) Also, you want all 5 of the conservative "Ideological Thought" inventions to have fired.
When you are done with the above, start buying goods needed to promote Craftsmen, Clerks, and Capitalists. Then, if you are a monarchy/constitutional monarchy/dictatorship, switch to a socialist party and wait for the 5 socialist "Ideological Thought" inventions to fire. Depending how long phase 1 took and whether the Liberal Revolution happened yet, you should have from 25 to 40 plurality. Then, promote some capitalists or clerks, and set reforms to make yourself a democracy (constitutional monarchies need to take the extra step and become a dictatorship first; that is well-detailed elsewhere). If you have enough of a liberal majority to get the liberals into power, good. If not, promote some clerks (changing voting rights to Wealth right after you become a democracy makes this easier). A few days before the election starts, max out all the reforms except for work hours (those are bad for productivity). Once the liberals get elected, set the social spending to 0 as to not bankrupt yourself actually paying for those reforms. Now the liberal events from "Ideological Thought" should fire, getting you around 60 plurality. If you haven't promoted some capitalists in your larger states, do so. After a few months, capitalists should start building factories (They may actually do some railoroading first, if you have the technology for it. This is generally acceptable.). Once your factories are open, European factory workers will start migrating to your paradise. This will increase your exports, increasing the income of capitalists, leading to more factories and more exports. After a few years, your industrial base should be good enough to compete with the 'big boys'.
That first election as a democracy is the critical point. If you are getting farmer/laborer immigration once the liberals get elected, you are on the right track. Craftsmen and clerks are more likely to immigrate than farmers and craftsmen, so you just need to build factories for them. If you are not getting immigrants after the first election, then you spent too much time in the first phase. The US has already reached 100 plurality and is probably improving its reforms, European nations have generally gotten their act together, and so on.
The two key points to being a successful immigration magnet is the timing of the democratization, and the maximizing of RGO output in the first section. Because capitalist income depends on your total exports, which at first depend on RGO output, maximizing RGOs is your major priority.
The initial immigration is the most important, as that is what sets up the "critical mass" of exports and population needed for the exponential growth that immigration and capitalists can bring. A good time to democratize is in the early 1850s (Europe is wracked with revolts and is exporting population in droves), during the Crimean War (Britain, France, and Russia are all very loath to peace out of that war, getting their war exhaustion into 30s and above, bringing with it mass emigration), and the US Civil War (war exhaustion in the US makes it less of an immigration magnet, allowing you to steal 'their' immigrants).