Alistair makes a mention of it, and I believe Gaider confirmed that two wardens can't have children together. I'll see if I can find a link.
I found a forum conversation from the Dragon Age Wikia, and it has a link to a conversation that happened on this site, but I can't get the link to work properly. So I'll just post the passage I found there:
David Gaider wrote: A Grey Warden can have a child... just not with another Grey Warden. So in the case of Alistair being married to a female PC the only possible result is no heir (unless Alistair has a child with someone other than his wife, I suppose). Grey Wardens have a limited chance of conception with a non-Grey Warden, but it does happen... and the child is not tainted in any fashion.
Insofar as how long a Grey Warden could remain on the throne, it depends. The taint will make a Grey Warden age faster, so someone like Loghain isn't going to be able to stay a Grey Warden for very long as he's no young man. The "thirty years" quote is about the maximum, but the reality is that it depends on how often one is exposed to the corruption and sometimes just personal variance-- even so, for a monarch to stay on the throne upwards of thirty years is no mean feat. I don't really think that's the limiting factor when it comes to this sort of thing.
Demeira wrote: Well, there goes my fairy tale! I was hoping for a loophole somewhere that would make my fanfiction plausible. I had this all planned out that Alistair and Orlaine (my PC) would have twins because of some ancient Tevinter fertility charms given to them by some sorceress out of Orlais and somehow the act of having these children born of two Wardens would somehow give Alistair and Orlaine an additional 20 years and would somehow dilute the taint. And these twins would start bloodlines that would play into the next two Blights. Looks like that idea is scrapped...
David Gaider wrote: Well... just because it's never happened doesn't mean it never could, I suppose. There are always exceptions. So if you involve some mysterious Tevinter fertility charm... why not? Really I'm just talking about the fact that Grey Wardens never produce offspring together naturally. Unnaturally is an entirely different story.
I'll point out that Alistair does bring this up, and in fact breaks up with a female player because he feels it's his duty to bear children -- unless she convinces him that there are more important things, like being happy.
If being able to marry the man you love is insufficient because you must also bear his children in order for you to be happy, then sure. I guess you'll be unhappy -- barring some kind of unforeseen circumstance occuring.
And my second post was not a pat-pat on the poster's head to make her feel better... there are always ways that these sorts of rules can get circumvented. Alistair did not, after all, say to you "two Grey Wardens cannot have children, except for the extremely rare possibility of them recovering the Holy Elixir of Saradesh or somehow purging their blood of the taint through unknown sorts of blood magic... but normally? Not a chance."
As far as anyone (including Alistair) knows, under normal circumstances two Grey Wardens cannot have children with each other. I didn't mention unknown exceptions because they're unknown -- that should just be assumed. And that's just the way it is.