Unfortunately not. Unlike a guy's penis that can be fondled from the pocket of his trousers, breasts have a much greater public profile.
I suppose you could move to a part of the world with a cold climate.
You might experiment and go bra-less. Having the material of a blouse or shirt rubbing over your nipples may make them hard, although, I doubt it will be constantly--still, probably quite a bit of the time. Then, again, you run into the problem guys have with an uncircumcised penis--that being an overall lack of sensitivitiy over time due to the constant friction of their clothing rubbing against the glans of their penis.
Why do you want them to always be erect? Seems to me that making them that way is a huge part of the fun. I keep telling people that what many women enjoy is the control they have over a man's penis being able to make him speed up or slow down or stop by the wayside on the road to making his climax happen more quickly or delayed. The same can be true for nipples. I urge you to reconsider even if it was possible for them to be erect all the time.
If you are interested in having them poke against your blouse or shirt, then consider the attention having a person's eyes always looking "there" might cause. It might be fun sometimes, other times, it can be embarrassing and uncomfortable for the guy who just can't takes his eyes off those peaks in an otherwise smooth profile. Just a thought or two.
Young girls have been known to stuff their bras with tissue in order to enhance what has yet to be. You might consider stuffing something in your bra to mimic two erect nipples--thimbles perhaps?
I think there are more practical things to be concerned about, like knowing all the information listed in the Index as examples.