Derive a public EC key from two public EC keys
As long as there is a probability that the adversary has the access to a valid signature on the message $m$ using one of the private keys, none of the schemes would be secure, and also any other scheme which is using a linear combination of the keys as the resulting private key.

Because, if an adversary has two valid ECDSA signatures on message $m$ which one is made by private key $a_1$ and the other is made by private key $a_2$, she can produce any signature on message $m$ using the private key $c=b_1a_1+b_2a_2+b_3$ where $b_1$,$b_2$ and $b_3$ are known to the adversary. This is due to the homomorphic properties of Elgemal signature.

So other than the algorithm #2 the algorithm #1 (Addition) seems to be unsecure. Whereas, If an adversary has a valid ECDSA signature on message $m$ using private key $a_1$ and she knows $a_2$ then it can produce a valid signature on message $m$ using private key $c=a_1+a_2$ quit efficiently. In other words for breaking the scheme it suffices to have just one of the private keys, say $a_2$, and a valid signature produced using the other private key, say $a_1$.

For making the answer more concise, I'm using the notations in Wikipedia article ~ "Elliptic Curve DSA".

assume the signature on message $m$ made using private key $a_1$ is $(r,s)$ and the forged signature made for private key $c=a_1+a_2$ is $(r',s)$.

$(r,y_1)=kG=zs^{-1}G+rs^{-1}a_1G$

$(r',y_1')=(r,y_1)+rs^{-1}a_2G$