Better sheet APIs for 10.8. Any resemblance to Mavericks is purely coincidental.

NSWindow+BetterSheets.h

//
//  NSWindow+BetterSheets.h
//  Gistapo
//
//  Created by Brent Royal-Gordon on 7/12/13.
//  Copyright (c) 2013 Architechies. All rights reserved.
//

#import <Cocoa/Cocoa.h>

#ifndef AVAILABLE_MAC_OS_VERSION_10_9_AND_LATER
enum {
    NSModalResponseStop                 = (-1000), // Also used as the default response for sheets
    NSModalResponseAbort                = (-1001),
    NSModalResponseContinue             = (-1002), 
};
typedef NSInteger NSModalResponse;
#endif

@interface NSWindow (BetterSheets)

- (void)beginSheet:(NSWindow *)sheetWindow completionHandler:(void (^)(NSModalResponse returnCode))handler;
- (void)beginCriticalSheet:(NSWindow *)sheetWindow completionHandler:(void (^)(NSModalResponse returnCode))handler __attribute__((unavailable ("-beginCriticalSheet:completionHandler: not implemented by NSWindow+BetterSheets")));
- (void)endSheet:(NSWindow *)sheetWindow;
- (void)endSheet:(NSWindow *)sheetWindow returnCode:(NSModalResponse)returnCode;
- (NSArray *)sheets; // An ordered array of the sheets on the window. This consists of the presented sheets in top-to-bottom order, followed by queued sheets in the order they were queued. This does not include nested/sub-sheets.
- (NSWindow *)sheetParent;

@end

NSWindow+BetterSheets.m

//
//  NSWindow+BetterSheets.m
//  Gistapo
//
//  Created by Brent Royal-Gordon on 7/12/13.
//  Copyright (c) 2013 Architechies. All rights reserved.
//

#import "NSWindow+BetterSheets.h"

@interface ArchSheetManager : NSObject

@property (weak) NSWindow * window;

@property (strong) NSMutableArray * enqueuedSheets;
@property (strong) NSMutableArray * enqueuedCompletionHandlers;

- (void)enqueueSheet:(NSWindow*)sheet completionHandler:(void (^)(NSModalResponse))completion;
- (void)enqueueCriticalSheet:(NSWindow*)sheet completionHandler:(void (^)(NSModalResponse))completion;
- (void)dequeueSheet:(NSWindow*)sheet returnCode:(NSModalResponse)returnCode;

- (void)sheetDidEnd:(NSWindow *)sheet returnCode:(NSInteger)returnCode contextInfo:(void *)contextInfo;

@end


#import <objc/runtime.h>

@implementation NSWindow (BetterSheetsConditional)

- (ArchSheetManager*)arch_sheetManager {
    ArchSheetManager * manager = objc_getAssociatedObject(self, _cmd);
    if(!manager) {
        manager = [ArchSheetManager new];
        manager.window = self;
        self.arch_sheetManager = manager;
    }
    return manager;
}

- (void)setArch_sheetManager:(ArchSheetManager*)sheetManager {
    objc_setAssociatedObject(self, @selector(arch_sheetManager), sheetManager, OBJC_ASSOCIATION_RETAIN);
}

- (void)arch_beginSheet:(NSWindow *)sheetWindow completionHandler:(void (^)(NSModalResponse))handler {
    [self.arch_sheetManager enqueueSheet:sheetWindow completionHandler:handler];
}

- (void)arch_beginCriticalSheet:(NSWindow *)sheetWindow completionHandler:(void (^)(NSModalResponse))handler {
    [self.arch_sheetManager enqueueCriticalSheet:sheetWindow completionHandler:handler];
}

- (void)arch_endSheet:(NSWindow *)sheetWindow {
    [self endSheet:sheetWindow returnCode:NSModalResponseStop];
}

- (void)arch_endSheet:(NSWindow *)sheetWindow returnCode:(NSModalResponse)returnCode {
    [self.arch_sheetManager dequeueSheet:sheetWindow returnCode:returnCode];
}

- (NSWindow *)arch_sheetParent {
    if(self.arch_sheetManager.window == self) {
        return nil;
    }
    return self.arch_sheetManager.window;
}

- (NSArray *)arch_sheets {
    return self.arch_sheetManager.enqueuedSheets;
}

static void ArchInstallMethodUnlessExists(Class class, SEL final) {
    if(class_respondsToSelector(class, final)) {
        return;
    }
    
    SEL original = NSSelectorFromString([NSString stringWithFormat:@"arch_%@", NSStringFromSelector(final)]);
    
    Method m = class_getInstanceMethod(class, original);
    class_addMethod(class, final, method_getImplementation(m), method_getTypeEncoding(m));
}

+ (void)load {
    ArchInstallMethodUnlessExists(self, @selector(beginSheet:completionHandler:));
    ArchInstallMethodUnlessExists(self, @selector(beginCriticalSheet:completionHandler:));
    ArchInstallMethodUnlessExists(self, @selector(endSheet:));
    ArchInstallMethodUnlessExists(self, @selector(endSheet:returnCode:));
    ArchInstallMethodUnlessExists(self, @selector(sheetParent));
    ArchInstallMethodUnlessExists(self, @selector(sheets));
}

@end

@implementation ArchSheetManager

- (id)init {
    if((self = [super init])) {
        self.enqueuedSheets = [NSMutableArray new];
        self.enqueuedCompletionHandlers = [NSMutableArray new];
    }
    return self;
}

- (void)addSheetToQueue:(NSWindow *)sheet completionHandler:(void (^)(NSModalResponse))completion {
    if(!completion) {
        completion = ^(NSModalResponse response){};
    }
    
    [self.enqueuedSheets addObject:sheet];
    [self.enqueuedCompletionHandlers addObject:[completion copy]];
    
    sheet.arch_sheetManager = self;
}

- (void)enqueueSheet:(NSWindow *)sheet completionHandler:(void (^)(NSModalResponse))completion {
    [self addSheetToQueue:sheet completionHandler:completion];
    if(sheet == self.enqueuedSheets[0]) {
        [NSApp beginSheet:sheet modalForWindow:self.window modalDelegate:self didEndSelector:@selector(sheetDidEnd:returnCode:contextInfo:) contextInfo:NULL];
    }
}

- (void)enqueueCriticalSheet:(NSWindow *)sheet completionHandler:(void (^)(NSModalResponse))completion {
    NSAssert(NO, @"Critical sheets NYI");
}

- (void)dequeueSheet:(NSWindow *)sheet returnCode:(NSModalResponse)returnCode {
    if(self.enqueuedSheets[0] == sheet) {
        [NSApp endSheet:sheet returnCode:returnCode];
    }
    else {
        [self doDequeueSheet:sheet returnCode:returnCode];
    }
}

- (void)doDequeueSheet:(NSWindow *)sheet returnCode:(NSModalResponse)returnCode {
    NSUInteger index = [self.enqueuedSheets indexOfObject:sheet];
    NSAssert(index != NSNotFound, @"Can't dismiss a sheet that hasn't been enqueued");
    
    void (^completion)(NSModalResponse) = self.enqueuedCompletionHandlers[index];
    completion(returnCode);
    
    sheet.arch_sheetManager = nil;
    
    [self.enqueuedCompletionHandlers removeObjectAtIndex:index];
    [self.enqueuedSheets removeObjectAtIndex:index];
}

- (void)sheetDidEnd:(NSWindow *)sheet returnCode:(NSInteger)returnCode contextInfo:(void *)contextInfo {
    NSParameterAssert(sheet == self.enqueuedSheets[0]);
    
    [sheet orderOut:self.window];
    [self doDequeueSheet:sheet returnCode:returnCode];
    
    if(self.enqueuedSheets.count) {
        [NSApp beginSheet:self.enqueuedSheets[0] modalForWindow:self.window modalDelegate:self didEndSelector:@selector(sheetDidEnd:returnCode:contextInfo:) contextInfo:NULL];
    }
}

@end

Hi, are you willing to place this code under a BSD or MIT license or similar?