I have shortened the chain, lengthened the chain etc. It finally flushes O.K. & the bowl clears if I hold the handle down for a little bit, the flapper seats then bobs back up and has to be manually pushed down, then it stays. It is a new flapper

Sounds like the flapper is not seating just right. Did you remove the rubber ring and hook the flapper on the ears of the overflow pipe?

Most after market flappers fit most toilets but some toilets are a little different than others. Some brands of flappers are a little different than others. You may have to try a different brand of flapper. You may even have to get one made by the manufacturer of the brand of toilet you have.

Did you remove the ring before installing the flapper? (see image). You MUST remove the ring before installing the flapper on the hooks. Good luck, Tom

Yes we removed the ring and the only writing on the toilet to indicate the brand is Made in Equador. The darn flapper just won't stay down unless I push it down.

Sounds like your flapper linkage needs adjusting.
With the flapper seated the linkage wants to have 1/4" of play. Too much play and the flapper doesn't get pulled back enough giving you a short flush. Too tight and it lets water seep past the flapper. I adjust the chain by the link and if it needs fine tuning, I bend the flush lever rod a bit until I have the desired play in the linkage.
You probably have already adjusted the linkage but In just had to ask. Does all the water leave the tank and the flapper still won't seat?
Is the flush lever free with no hang ups? Back to you. Tom

Yes I've changed the linkage a lot, short long and between. It flushes, clears the bowl, the flapper seals THEN it pops back up and just stays up about 1/4 to 1/2" and the water just runs through. The flush lever is free. We are almost ready to buy a new toilet...

Don't buy a new toilet. The bowl and tank don't were out. Start by replacing the tank parts beginning with the flapper. That should do it but if it doesn't the next fitting I'd replace would be them flush valve. Only one more part remains ,the flush lever, and you've replaced all the parts that have to do with discharging the tank. Good luck. Tom

Finally got an anxwer to the toilet flap popping back up after it had seated. The water pressure was to high. We turned down the spigot a little and it works great! That tip came from a plumber recommended by Rosie On The House. THANKS

Flapper finally stays down, the water pressure was to high. Turned the spigot down and flap stays down. HOORAY.

Not pressure but maybe volume was too strong. Partially closing a valve or stop does not alter the pressure one bit. Please tell us why the flapper was replaced since you said it was new

I was using "pressure" and "volume" as the same function. The water was entering the tank to hard & fast and unseating the flap. We kept replacing the flap because we thought that was the cause. All is good now.

That's OK many folks do the same but they are quite different to those of us who work on plumbing