Nicaraguan-born child, one or more US parents and Nicaraguan parent's earlier children
If you're the father of a Nicaraguan child, apparently legit or not, you can register the birth and get the US citizenship, but probably will have to have a DNA test if the Embassy is suspicious.
http://www.travel.state.gov/law/citizenship/citizenship_5199.html is a further link to this:
"Birth Abroad Out-of-Wedlock to a U.S. Citizen Father – “New” Section 309(a)
A person born abroad out-of-wedlock to a U.S. citizen father may acquire U.S. citizenship under Section 301(g) of the INA, as made applicable by the “new” Section 309(a) of the INA provided:
A blood relationship between the person and the father is established by clear and convincing evidence; The father had the nationality of the United States at the time of the person’s birth; The father was physically present in the United States or its outlying possessions prior to the child’s birth for five years, at least two of which were after reaching the age of 14. The father (unless deceased) has agreed in writing to provide financial support for the person until the person reaches the age of 18 years, and While the person is under the age of 18 years -- the person is legitimated under the law of his/her residence or domicile, the father acknowledges paternity of the person in writing under oath, or the paternity of the person is established by adjudication of a competent court."
Apparently the law has changed in 1986, which would be when at least some US fathers were trying to reunite with their Vietnamese born children.
In all cases, the consular officials investigating the cases may ask for DNA tests which are generally quite conclusive in proving who the parents really are (prior paternity test were based on blood types which were more conclusive in ruling out people as impossible parents than proving the man was the parent).
I think Phil covered the gotchas for having US citizenship. German father/Nicaraguan mother -- the charges are something like 800 Euros for registering the birth. Other countries may not allow fathers to claim foreign born children with non-national mothers -- see other countries websites for more details.
More information on what exactly a parent or parents will need at the consular meeting:
Note that the baby or child needs to be with you at application. If both parents can't be present, the parent who isn't there needs to sign off on the arrangement. Total fees at this time are $205 (certification and passport). You may claim your children up to their 18th birthdays. I'd misremembered that this had to be done a short time after birth. There may be other Nicaraguan legal fees in establishing paternity.
The liability to the guy is that he is also agreeing to child support until the child is 18.
Phil has already covered the liabilities of being a US citizen which are more pertinent if the child never lives in the US. If a child wants to live in the US, being a citizen makes the process quite a bit simpler.
Immigrant visa information for adopted children here: http://www.uscis.gov/portal/site/uscis/menuitem.eb1d4c2a3e5b9ac89243c6a7... Obviously, several different avenues for this, some which seem to apply to men who would like to adopt their wives' earlier children.
Nicaragua's policy is not encouraging foreign adoptions (the fiasco in Guatemala with stolen babies and high fees that made the brokers rich being part of why), but in practice, seems willing to work with people who have either agreed to live in Nicaragua until the child is 18 or who have permission from the US government to adopt. Both countries do change these laws from time to time, so check the websites and the US embassy and Nicaraguan child and family agencies for best current information.
I don't know what recourse Nicaraguan women would have if the US citizen fathers refused to acknowledge the children the men sired. Juanno or Paul? It looks like the US citizen father has to decide to declare that he is the father and agree to present the child at the Embassy. Not sure there's a mechanism for forcing US citizen fathers to acknowledge paternity.