There are plenty of co-ops in Manhattan that allow guarantors. I have some listings like that right now. Parents buying for children, or children buying for senior parents, or pied-a-terres, are all very common and can be found at very nice buildings with great apartments.
However, if you have your eye on an apartment in a co-op that specifically does not allow this kind of arrangement, you will not be able to buy the unit. Co-op boards cannot make exceptions or they could be subject to lawsuits, so they don't do it. I would advise you not to waste time and money trying to get into a co-op with that policy.
Condominiums are another story. There is an application process at condos, but the managers do not have the power that co-op boards have. Rarely they try to assert such power, but whether they can legally get away with it is unclear. In general you should have no resistance to this with condos.
Co-ops tend to be less expensive than condos, in part because they are more restrictive and to many (not all) that makes them less desirable.
If you contact me, I can help you find apartments that accept this kind of arrangement. Since you live in Sutton Place you already know that most co-ops require at least 20% down payment (some require much more) and a solid financial base. With condos, usually you can purchase so long as you have the financing from any source.