You have to be emperor of Byzantium and be Christian for the decision to restore the Roman Empire to show up. From decisions/realm_decisions.txt:

restore_roman_empire = {
    [...]
    potential = {
        has_dlc = "Legacy of Rome"
        age = 16
        prisoner = no
        NOT = { trait = incapable }
        has_landed_title = e_byzantium
        religion_group = christian
    }
    [...]
}

If you don't like that, you can simply remove or comment out the religion_group line.

Increasing your levies

You can change your church/city/feudal laws to allow you to raise more levies.

Increasing your domain

You could perhaps focus a bit on non-British lands for a while. Get some holdings in France or in the Benelux. This will give you more levies (in the long run), but it might also create problems. In an inevitable war, it means the HRE would have continental provinces they could siege – they would then act as a diversion (less troops for their British invasion) but also a ticking war score for them.

Destroy it from within

Use your chancellor to sow discontent. The HRE is vast, and someone is bound to already have an itch for the Emperor. With luck, you can spark a rebellion for him to worry about.

You might also consider arranging a tragic accident for the good Emperor. Depending on their situation, a well-timed death might end up in a sucession crisis. The HRE is elective, but I guess it still applies.

Get better friends

If you have a few daughters to spare, you could marry them off for beter allies. I would focus on allies that can actually make an impact (France, Poland, maybe Hungary or one of the Scandinavian countries depending on your game).

Get divine friends

Become BFF with the Pope, and have him excommunicate the Emperor. This means everybody has a free CB. Also: perhaps you can hire Holy Orders? (no time to check).

Arrange a hostile takeover (expert level)

This one is tricky with the HRE, since its an elective imperial state, but with a lot of cunning (and probably some mysterious deaths), you might be able to place your heir on the throne. This strategy is more effective with realms that are smaller than yours, since they are more likely to accept your propositions and generally have more foreseeable succession laws.

Be patient (best in test!)

You don't want to fight this behemoth on your own. Wait untill they have other wars to worry about, preferably against powerful opponents such as France or Poland, or better yet civil war. In my game, the HRE would disintegrate every 15-20 years or so, due to internal strife. That would be an ideal moment to strike.

War strategy

I guess you could easilly defeat any Imperial troops on the isles, the problem would be reinforcements from the continent. So what I would probably do, is to plan a Blitzkrieg on the Isles, and make sure to occupy the provinces in the war goal without losing too many troops.

The HRE will probably not land a 90k stack on British soil all at once. In fact, they might not even have enough sea provinces to raise a navy large enough to transport large armies. So create a doom stack of strong Irish patriots, and place it conveniently close to where you expect them to land – and then pounce their puny 10k armies with your massive 30k!

Rinse and repeat untill they run out of men, or the war goal is sufficiently high.